Using nonlocal interface problem allows for 7x speedup in large-scale simulations

Analytic solutions u 2D 0,0 for s = 0.4 and u 2D 1,1 for s = 0.6. The behaviour (3.17) close to the boundary is apparent.

Multimaterial problems exist in mission applications such as mechanics and subsurface transport. To capture effects arising from long-range forces at the microscale and mesoscale that aren’t accounted for by classical partial differential equations, the MAThematical foundations for Nonlocal Interface Problems (MATNIP) project team developed a mathematically rigorous interface theory employing nonlocal models that use integral as opposed to differential operators. By applying their theory to domain decomposition methods, the team was able to achieve speedups of up to 7x in solve in solve time in large-scale simulations. The issue of parameter selection for nonlocal models from experimental data was successfully tackled using both adjoint optimization and ML approaches.

The Sandia team collaborated with Los Alamos and Oak Ridge National Laboratories, as well as Florida State University, Sandia Alliance partner University of Texas at Austin, and Lehigh University. The project team had fifteen publications, presented talks, and a former team member, Marta D’Elia, was nominated for the SIAM Wilkinson Price in Scientific Computing and Numerical Analysis for contributions to nonlocal modeling.

Sandia researchers linked to work

  • Christian Glusa
  • Mamikon Gulian
  • Pavel Bochev
  • Mario Martinez

Sponsored by

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Publications

  • de Castro, A., Kuberry, P., Tezaur, I., Bochev, P., & Bochev, P. (2023). A Novel Partitioned Approach for Reduced Order Model—Finite Element Model (ROM-FEM) and ROM-ROM Coupling. Earth and Space 2022. https://doi.org/10.1061/9780784484470.044 Publication ID: 80830
  • D’Elia, M., Gulian, M., Mengesha, T., Scott, J.M., & Scott, J.M. (2022). Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition. Fractional Calculus and Applied Analysis. https://doi.org/10.2172/1855046 Publication ID: 77052
  • D’Elia, M., Glusa, C., & Glusa, C. (2022). A fractional model for anomalous diffusion with increased variability: Analysis, algorithms and applications to interface problems. Numerical Methods for Partial Differential Equations, 38(6), pp. 2084-2103. https://doi.org/10.1002/num.22865 Publication ID: 75443
  • D’Elia, M., Bochev, P., Foster, J., Glusa, C., Gulian, M., Gunzburger, M., Trageser, J., Kuhlman, K., Martinez, M., Najm, H.N., Silling, S., Tupek, M., Xu, X., & Xu, X. (2022). Mathematical Foundations for Nonlocal Interface Problems: Multiscale Simulations of Heterogeneous Materials (Final LDRD Report). https://doi.org/10.2172/1888162 Publication ID: 80232
  • Mahadevan, V.S., Guerra, J.E., Jiao, X., Kuberry, P., Li, Y., Ullrich, P., Marsico, D., Jacob, R., Bochev, P., Jones, P., & Jones, P. (2022). Metrics for Intercomparison of Remapping Algorithms (MIRA) protocol applied to Earth system models. Geoscientific Model Development, 15(17), pp. 6601-6635. https://doi.org/10.5194/gmd-15-6601-2022 Publication ID: 80860
  • Burkovska, O., Glusa, C., D’Elia, M., & D’Elia, M. (2022). An optimization-based approach to parameter learning for fractional type nonlocal models. Computers and Mathematics with Applications, 116, pp. 229-244. https://doi.org/10.1016/j.camwa.2021.05.005 Publication ID: 78671
  • D’Elia, M., Glusa, C., Xu, X., Foster, J., & Foster, J. (2022). Machine-Learning of Nonlocal Kernels for Anomalous Subsurface Transport from Breakthrough Curves. https://doi.org/10.2172/1842267 Publication ID: 79996
  • Suzuki, J.L., Gulian, M., Zayernouri, M., D’Elia, M., & D’Elia, M. (2022). Fractional Modeling in Action: a Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials. Journal of Peridynamics and Nonlocal Modeling. https://doi.org/10.2172/1820001 Publication ID: 75627
  • Gulian, M., Frankel, A., Swiler, L., & Swiler, L. (2022). Gaussian process regression constrained by boundary value problems. Computer Methods in Applied Mechanics and Engineering, 388. https://doi.org/10.1016/j.cma.2021.114117 Publication ID: 75489
  • Xu, X., Glusa, C., D’Elia, M., Foster, J.T., & Foster, J.T. (2021). A FETI approach to domain decomposition for meshfree discretizations of nonlocal problems. Computer Methods in Applied Mechanics and Engineering, 387. https://doi.org/10.1016/j.cma.2021.114148 Publication ID: 75442
  • Glusa, C. (2021). PyNucleus – A FEM code for nonlocal problems [Conference Presenation]. https://doi.org/10.2172/1900339 Publication ID: 76959
  • D’Elia, M., Bochev, P., Perego, M., Trageser, J., Littlewood, D., & Littlewood, D. (2021). An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions. https://doi.org/10.2172/1825041 Publication ID: 76166
  • Sockwell, K., Kuberry, P., Tucker, J., Bochev, P., & Bochev, P. (2021). Automated Discovery of DOminaNt physics Informed Surrogates (ADDONIS) Framework [Presentation]. https://www.osti.gov/biblio/1894021 Publication ID: 76392
  • Acer, S., Boman, E., Glusa, C., Rajamanickam, S., & Rajamanickam, S. (2021). Sphynx: A parallel multi-GPU graph partitioner for distributed-memory systems [Conference Presenation]. Parallel Computing. https://doi.org/10.2172/1853867 Publication ID: 77409
  • Hembree, C., Hanson, J., Paskaleva, B., Bochev, P., Keiter, E., Mar, A., Mei, T., & Mei, T. (2021). Semiconductor Device Models Constructed Using Simple Elements and Auxiliary Dynamics [Conference Presenation]. https://doi.org/10.2172/1890913 Publication ID: 75902
  • Kuberry, P., Mei, T., Keiter, E., Paskaleva, B., Bochev, P., Hanson, J., & Hanson, J. (2021). Xyce Python Model Interpreter (Xyce-PyMi) for enabling ML advancements in production circuit simulation software [Conference Presenation]. https://doi.org/10.2172/1889549 Publication ID: 75928
  • Gulian, M. (2021). Robust architectures, initialization, and training for deep neural networks via the adaptive basis interpretation [Conference Presenation]. https://doi.org/10.2172/1889595 Publication ID: 75730
  • Acer, S., Boman, E., Glusa, C., Rajamanickam, S., & Rajamanickam, S. (2021). Sphynx: a parallel multi-GPU graph partitioner [Conference Presenation]. https://doi.org/10.2172/1882077 Publication ID: 79650
  • Gulian, M. (2021). Data-driven learning of nonlocal physics from high-fidelity synthetic data [Conference Presenation]. https://doi.org/10.2172/1888123 Publication ID: 75404
  • Hu, J., Glusa, C., & Glusa, C. (2021). Recent Advances in Maxwell Solvers for PIC Simulations Across Architectures [Conference Presenation]. https://doi.org/10.2172/1888437 Publication ID: 79110
  • Loe, J.A., Glusa, C., Yamazaki, I., Boman, E., Rajamanickam, S., & Rajamanickam, S. (2021). Properties of GMRES with Iterative Refinement on GPUs [Conference Presenation]. https://doi.org/10.2172/1884157 Publication ID: 79139
  • D’Elia, M., Olson, H., Gulian, M., & Gulian, M. (2021). Comparison of Tempered and Truncated Fractional Models [Conference Poster]. https://doi.org/10.2172/1888466 Publication ID: 79402
  • Gulian, M. (2021). Partition of Unity Networks for Deterministic and Probabilistic Regression [Presentation]. https://www.osti.gov/biblio/1888667 Publication ID: 79485
  • Gulian, M. (2021). Robust architectures, initialization, and training for deep neural networks [Presentation]. https://www.osti.gov/biblio/1888396 Publication ID: 79244
  • Gulian, M. (2021). Gaussian Process Regression constrained by Boundary Value Problems [Conference Presenation]. https://doi.org/10.2172/1883509 Publication ID: 79507
  • Hanson, J., Paskaleva, B., Bochev, P., Keiter, E., Hembree, C., Kuberry, P., & Kuberry, P. (2021). A Numerical Compact Photocurrent Model and its Implementation via Xyce-PyMi [Conference Presenation]. https://doi.org/10.2172/1876997 Publication ID: 79274
  • Loe, J.A., Glusa, C., Yamazaki, I., Boman, E., Rajamanickam, S., & Rajamanickam, S. (2021). Experimental Evaluation of Multiprecision Strategies for GMRES on GPUs [Conference Paper]. 2021 IEEE International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2021 – In conjunction with IEEE IPDPS 2021. https://doi.org/10.1109/IPDPSW52791.2021.00078 Publication ID: 77887
  • Sockwell, K., Bochev, P., Peterson, K., Kuberry, P., & Kuberry, P. (2021). The Interface-Flux-Recovery (IFR) Methodfor Conservative and Stable Coupling Schemesin Geophysical Fluids and Mechanics [Conference Presenation]. https://doi.org/10.2172/1877832 Publication ID: 78801
  • Cyr, E., Gulian, M., Lee, K., Patel, R.G., Perego, M., Trask, N., & Trask, N. (2021). An Adaptive Basis Perspective to Improve Initialization and Accelerate Training of DNNs [Presentation]. https://www.osti.gov/biblio/1872708 Publication ID: 78814
  • Glusa, C. (2021). A Fractional Model for Anomalous Diffusion with Increased Variability [Conference Presenation]. https://doi.org/10.2172/1873280 Publication ID: 78836
  • Bochev, P. (2021). A hybrid analytic-numerical compact model for radiation-induced photocurrent effects [Presentation]. https://www.osti.gov/biblio/1884185 Publication ID: 78609
  • Gulian, M. (2021). Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport [Conference Presenation]. https://doi.org/10.2172/1870369 Publication ID: 78630
  • Loe, J.A., Glusa, C., Yamazaki, I., Boman, E., Rajamanickam, S., & Rajamanickam, S. (2021). Experimental Evaluation of Multiprecision Strategies for GMRES on GPUs [Conference Presenation]. https://doi.org/10.2172/1869548 Publication ID: 78515
  • Siefert, C., Tuminaro, R., Glusa, C., Kaushagen, J., & Kaushagen, J. (2021). Multilevel Methods for Maxwell’s Equations [Conference Presenation]. https://doi.org/10.2172/1869378 Publication ID: 78523
  • Gulian, M. (2021). Robust architectures initialization and training for deep neural networks via the adaptive basis interpretation [Presentation]. https://www.osti.gov/biblio/1866561 Publication ID: 78329
  • Glusa, C. (2021). Optimal Control for the Fractional Laplacian [Conference Presenation]. https://doi.org/10.2172/1853869 Publication ID: 77411
  • Kuberry, P., Peterson, K., Bochev, P., & Bochev, P. (2021). Generalized Moving Least Squares (GMLS) with Clip and Assured Sum (CAAS) Post-processing for Earth System Remap [Conference Presenation]. https://doi.org/10.2172/1854070 Publication ID: 77433
  • Gulian, M. (2021). Data-driven learning of nonlocal physics from high-fidelity synthetic data [Conference Presenation]. https://doi.org/10.2172/1854073 Publication ID: 77436
  • Loe, J.A., Glusa, C., Yamazaki, I., Boman, E., Rajamanickam, S., & Rajamanickam, S. (2021). Multiprecision Krylov Solvers in Kokkos and Belos [Conference Presenation]. https://doi.org/10.2172/1854310 Publication ID: 77452
  • Berger-Vergiat, L., Hu, J., Glusa, C., Siefert, C., & Siefert, C. (2021). Portability of Nalu-Wind using Trilinos and Kokkos Libraries [Conference Presenation]. https://doi.org/10.2172/1854321 Publication ID: 77462
  • Gulian, M. (2021). A block coordinate descent optimizer for classification problems exploiting convexity [Conference Presenation]. https://doi.org/10.2172/1859695 Publication ID: 77748
  • You, H., Yu, Y., Trask, N., Gulian, M., D’Elia, M., & D’Elia, M. (2021). Data-driven learning of nonlocal physics from high-fidelity synthetic data. Computer Methods in Applied Mechanics and Engineering, 374. https://doi.org/10.1016/j.cma.2020.113553 Publication ID: 73539
  • Cyr, E., Gulian, M., Patel, R.G., Perego, M., Trask, N., & Trask, N. (2021). An Adaptive Basis Perspective to Improve Initialization and Accelerate Training of DNNs [Conference Presenation]. https://doi.org/10.2172/1847582 Publication ID: 77381
  • D’Elia, M., Bochev, P., & Bochev, P. (2021). Formulation, analysis and computation of an optimization-based local-to-nonlocal coupling method. Results in Applied Mathematics, 9. https://doi.org/10.1016/j.rinam.2020.100129 Publication ID: 53184
  • Swiler, L., Gulian, M., Frankel, A., Safta, C., Jakeman, J., & Jakeman, J. (2021). Constrained Gaussian Processes: A Survey [Conference Presenation]. https://doi.org/10.2172/1847480 Publication ID: 77280
  • D’Elia, M., Gulian, M., & Gulian, M. (2021). Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport. https://doi.org/10.2172/1763574 Publication ID: 75004
  • Patel, R.G., Trask, N., Gulian, M., Cyr, E., & Cyr, E. (2021). A block coordinate descent optimizer for classification problems exploiting convexity [Conference Paper]. CEUR Workshop Proceedings. https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85116653183&origin=inward Publication ID: 77621
  • Glusa, C., ANTIL, H., D’Elia, M., van Bloemen Waanders, B., Weiss, C., & Weiss, C. (2021). A fast solver for the fractional helmholtz equation. SIAM Journal on Scientific Computing, 43(2), pp. A1362-A1388. https://doi.org/10.1137/19M1302351 Publication ID: 75065
  • Glusa, C., D’Elia, M., & D’Elia, M. (2021). Nonlocal operators with variable coefficients [Conference Poster]. https://doi.org/10.2172/1854680 Publication ID: 75068
  • Gulian, M. (2021). A Unified Theory of Fractional Nonlocal and Weighted Nonlocal Vector Calculus [Conference Poster]. https://doi.org/10.2172/1841821 Publication ID: 75102
  • Glusa, C., OTAROLA, E., & OTAROLA, E. (2021). Error estimates for the optimal control of a parabolic fractional pde. SIAM Journal on Numerical Analysis, 59(2), pp. 1140-1165. https://doi.org/10.1137/19m1267581 Publication ID: 72369
  • Bettencourt, M.T., Brown, D.A.S., Cartwright, K.L., Cyr, E., Glusa, C., Lin, P.T., Moore, S., McGregor, D.A.O., Pawlowski, R., Phillips, E., Roberts, N.V., Wright, S.A., Maheswaran, S., Jones, J.P., Jarvis, S.A., & Jarvis, S.A. (2021). EMPIRE-PIC: A performance portable unstructured particle-in-cell code. Communications in Computational Physics, 30(4), pp. 1232-1268. https://doi.org/10.4208/cicp.oa-2020-0261 Publication ID: 77552
  • Glusa, C., Boman, E., Chow, E., Rajamanickam, S., Szyld, D.B., & Szyld, D.B. (2020). Scalable asynchronous domain decomposition solvers. SIAM Journal on Scientific Computing, 42(6), pp. C384-C409. https://doi.org/10.1137/19m1291303 Publication ID: 74483
  • Kookjin, L., Trask, N., Patel, R.G., Gulian, M., Cyr, E., & Cyr, E. (2020). Partition of unity networks: data-driven meshfree hp-approximation [Conference Paper]. https://www.osti.gov/biblio/1835970 Publication ID: 72183
  • Loe, J.A., Glusa, C., Yamazaki, I., Boman, E., Rajamanickam, S., & Rajamanickam, S. (2020). Mixed-Precision GMRES in Trilinos [Conference Presenation]. https://doi.org/10.2172/1833786 Publication ID: 71988
  • Loe, J.A., Glusa, C., Boman, E., Yamazaki, I., Rajamanickam, S., & Rajamanickam, S. (2020). Multiprecision Krylov Solvers in Trilinos [Presentation]. https://www.osti.gov/biblio/1829961 Publication ID: 71611
  • Loe, J.A., Glusa, C., Boman, E., Yamazaki, I., Rajamanickam, S., & Rajamanickam, S. (2020). Multiprecision GMRES in Trilinos packages Belos and Kokkos [Conference Presenation]. https://doi.org/10.2172/1832692 Publication ID: 71889
  • Sockwell, K., Peterson, K., Bochev, P., Kuberry, P., & Kuberry, P. (2020). Bulk-Interface-Flux-Recovery (Bulk-IFR) Methodfor Coupling the Atmosphere-Ocean Interface [Conference Presenation]. https://doi.org/10.2172/1832721 Publication ID: 71898
  • Sockwell, K.C., Peterson, K., Kuberry, P., Bochev, P., Trask, N., & Trask, N. (2020). Interface Flux Recovery coupling method for the ocean–atmosphere system. Results in Applied Mathematics, 8. https://doi.org/10.1016/j.rinam.2020.100110 Publication ID: 73208
  • Kuberry, P., Trask, N., Koester, J.J., Bochev, P., & Bochev, P. (2020). Regression Based Approach for Robust Finite Element Analysis on Arbitrary Grids (REBAR) [Conference Poster]. https://www.osti.gov/biblio/1822641 Publication ID: 70985
  • Bochev, P., Ridzal, D., D’Elia, M., Perego, M., Peterson, K., & Peterson, K. (2020). Optimization-based, property-preserving finite element methods for scalar advection equations and their connection to Algebraic Flux Correction. Computer Methods in Applied Mechanics and Engineering, 367. https://doi.org/10.1016/j.cma.2020.112982 Publication ID: 68885
  • Hanson, J., Bochev, P., Paskaleva, B., & Paskaleva, B. (2020). Learning Compact Physics-Aware Photocurrent Models Using Dynamic Mode Decomposition [Presentation]. https://doi.org/10.1002/sam.11485 Publication ID: 74536
  • Gulian, M., Swiler, L., Frankel, A., Safta, C., Jakeman, J., & Jakeman, J. (2020). A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges [Conference Poster]. https://www.osti.gov/biblio/1814448 Publication ID: 74592
  • Gulian, M., Cyr, E., Patel, R.G., Perego, M., Trask, N., & Trask, N. (2020). Robust training and initialization of deep neural networks: an adaptive basis viewpoint [Conference Poster]. https://www.osti.gov/biblio/1808257 Publication ID: 74043
  • Gulian, M., Swiler, L., Frankel, A., Jakeman, J., Safta, C., & Safta, C. (2020). A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges [Conference Poster]. https://www.osti.gov/biblio/1812282 Publication ID: 74359
  • Aadithya, K., Kuberry, P., Paskaleva, B., Bochev, P., Leeson, K., Mar, A., Mei, T., Keiter, E., & Keiter, E. (2020). Data-Driven Compact Models for Circuit Design and Analysis [Conference Poster]. https://www.osti.gov/biblio/1810271 Publication ID: 74199
  • Cyr, E., Gulian, M., Patel, R.G., Perego, M., Trask, N., & Trask, N. (2020). Robust Training and Initialization of Deep Neural Networks An Adaptive Basis Viewpoint [Conference Poster]. https://www.osti.gov/biblio/1810691 Publication ID: 74202
  • Hu, J., Glusa, C., & Glusa, C. (2020). One slide overviews of the Belos and MueLu Libraries in Trilinos [Presentation]. https://www.osti.gov/biblio/1810699 Publication ID: 74210
  • Patel, R.G., Trask, N., Gulian, M., Cyr, E., & Cyr, E. (2020). A block coordinate descent optimizer for classification problems exploiting convexity. Arxiv. https://www.osti.gov/biblio/1834091 Publication ID: 73782
  • Bochev, P. (2020). Data driven photocurrent models [Presentation]. https://www.osti.gov/biblio/1804988 Publication ID: 73925
  • Trask, N., Bochev, P., Perego, M., & Perego, M. (2020). A conservative, consistent, and scalable meshfree mimetic method. Journal of Computational Physics, 409. https://doi.org/10.1016/j.jcp.2019.109187 Publication ID: 67460
  • D’Elia, M., Du, Q., Glusa, C., Gunzburger, M., Tian, X., Zhou, Z., & Zhou, Z. (2020). Numerical methods for nonlocal and fractional models. Acta Numerica, 29, pp. 1-124. https://doi.org/10.1017/s096249292000001x Publication ID: 77290
  • Aadithya, K., Kuberry, P., Keiter, E., Bochev, P., Mar, A., Mei, T., Paskaleva, B., Leeson, K., & Leeson, K. (2020). Using ML to Develop Compact Models [Presentation]. https://www.osti.gov/biblio/1779603 Publication ID: 73330
  • Lischke, A., Pang, G., Gulian, M., Song, F., Glusa, C., Zheng, X., Mao, Z., Cai, W., Meerschaert, M.M., Ainsworth, M., Karniadakis, G.E., & Karniadakis, G.E. (2020). What is the fractional Laplacian? A comparative review with new results. Journal of Computational Physics, 404. https://doi.org/10.1016/j.jcp.2019.109009 Publication ID: 66165
  • Hu, J., Glusa, C., Moore, S., Lin, P., Phillips, E., Bettencourt, M.T., Elliott, J., Siefert, C., Rajamanickam, S., & Rajamanickam, S. (2020). Linear Solvers for Plasma Simulations on Advanced Architectures [Conference Poster]. https://www.osti.gov/biblio/1765804 Publication ID: 72530
  • Berger-Vergiat, L., Hu, J., Tuminaro, R., Siefert, C., Glusa, C., & Glusa, C. (2020). MueLu’s Algorithmic Performance on GPU [Conference Poster]. https://www.osti.gov/biblio/1766725 Publication ID: 72589
  • Kuberry, P., Bochev, P., Peterson, K., & Peterson, K. (2020). A virtual control, mesh-free coupling method for non-coincident interfaces [Conference Poster]. Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018. https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85081063173&origin=inward Publication ID: 62466
  • Kuberry, P., Perego, M., Trask, N., Bochev, P., & Bochev, P. (2020). Field reconstruction from Raviart-Thomas Nedelec and finite volume degrees-of-freedom using Generalized Moving Least Squares [Conference Poster]. https://www.osti.gov/biblio/1761038 Publication ID: 70722
  • Bochev, P., Trask, N., Kuberry, P., Perego, M., & Perego, M. (2020). Mesh-Hardened Finite Element Analysis Through a Generalized Moving Least-Squares Approximation of Variational Problems [Conference Poster]. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). https://doi.org/10.1007/978-3-030-41032-2_7 Publication ID: 67278
  • Anguiano, M., Kuberry, P., Bochev, P., Masud, A., & Masud, A. (2020). Synchronous and concurrent multidomain computing method for cloud computing platforms. SIAM Journal on Scientific Computing. https://doi.org/10.1137/20m1349278 Publication ID: 79092
  • Ridzal, D., Bochev, P., & Bochev, P. (2020). Optimization-based property-preserving solution recovery for fault-tolerant scalar transport [Conference Poster]. Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018. https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85081059417&origin=inward Publication ID: 62461
  • Aadithya, K., Kuberry, P., Paskaleva, B., Bochev, P., Leeson, K., Mar, A., Mei, T., Keiter, E., & Keiter, E. (2019). Development, Demonstration and Validation of Data-Driven Compact Diode Models for Circuit Simulation and Analysis. https://doi.org/10.2172/1592881 Publication ID: 66892
  • Cyr, E., Gulian, M., Patel, R.G., Perego, M., Trask, N., Ridzal, D., Guenther, S., Ruthotto, L., Schroder, J., Gauger, N., & Gauger, N. (2019). Improved Neural Network Training: Layer-Parallelism Least-squares and Initialization [Conference Poster]. https://www.osti.gov/biblio/1643364 Publication ID: 66945
  • Cyr, E., Gulian, M., Patel, R.G., Perego, M., Trask, N., & Trask, N. (2019). Robust Training and Initialization of Deep Neural Networks: An Adaptive Basis Viewpoint [Conference Poster]. https://www.osti.gov/biblio/1643463 Publication ID: 66738
  • Gulian, M., Raissi, M., Karniadakis, G., & Karniadakis, G. (2019). Machine Learning of Space-Fractional Differential Equations [Conference Poster]. https://doi.org/10.1137/18M1204991 Publication ID: 65842
  • Sockwell, K., Kuberry, P., Bochev, P., Trask, N., Peterson, K., & Peterson, K. (2019). Bulk-Interface-Flux-Recovery (Bulk-IFR) Method for Coupling the Atmosphere-Ocean Interface [Conference Poster]. https://www.osti.gov/biblio/1642998 Publication ID: 65903
  • D’Elia, M., Bochev, P., & Bochev, P. (2019). Formulation analysis and computation of an optimization-based local-to-nonlocal coupling method. https://doi.org/10.2172/1572228 Publication ID: 65904
  • Bochev, P., Bosler, P., Kuberry, P., Perego, M., Peterson, K., Trask, N., & Trask, N. (2019). Compatible Particle Discretizations. Final LDRD Report. https://doi.org/10.2172/1569143 Publication ID: 65024
  • Glusa, C., D’Elia, M., Antil, H., Weiss, C., van Bloemen Waanders, B., & van Bloemen Waanders, B. (2019). A Fast Solver for the Fractional Helmholtz Equation. https://doi.org/10.2172/1569144 Publication ID: 65029
  • Glusa, C. (2019). Asynchronous Domain Decomposition Solvers [Conference Poster]. https://www.osti.gov/biblio/1641965 Publication ID: 64835
  • Bochev, P., Trask, N., Perego, M., & Perego, M. (2019). Mimetic meshfree methods or how to be compatible without a mesh [Conference Poster]. https://www.osti.gov/biblio/1641675 Publication ID: 70529
  • Bochev, P., Kuberry, P., Trask, N., Perego, M., & Perego, M. (2019). The amazing powers of Generalized Moving Least-Squares [Conference Poster]. https://www.osti.gov/biblio/1641676 Publication ID: 70530
  • Aadithya, K., Kuberry, P., Keiter, E., Bochev, P., Mar, A., Mei, T., Paskaleva, B., Leeson, K., & Leeson, K. (2019). Data-driven Circuit Design From Electrical Measurement Data To Compact Device Models [Conference Poster]. https://www.osti.gov/biblio/1641510 Publication ID: 70299
  • Glusa, C., Glusa, C., Hu, J., Hu, J., & Hu, J. (2019). Krylov Solvers and Algebraic Multigrid [Presentation]. https://www.osti.gov/biblio/1645719 Publication ID: 70301
  • Tuminaro, R., Shadid, J.N., Cyr, E., Lin, P., Pawlowski, R., Phillips, E., Wiesner, T., Adler, J., Benson, T., Chacon, L., Farrell, P., Rappaport, A., MacLachlan, S., Hu, J., Berger-Vergiat, L., Glusa, C., Siefert, C., & Siefert, C. (2019). Scalable Preconditioners to Improve Time to Solution for Magnetohydrodynamics Applications [Presentation]. https://www.osti.gov/biblio/1645823 Publication ID: 70609
  • Peterson, K., Bochev, P., Kuberry, P., & Kuberry, P. (2019). Explicit synchronous partitioned algorithms for interface problems based on Lagrange multipliers. Computers and Mathematics with Applications, 78(2), pp. 459-482. https://doi.org/10.1016/j.camwa.2018.09.045 Publication ID: 60611
  • Hu, J., Glusa, C., & Glusa, C. (2019). Overview of the Trilinos packages Belos and MueLu [Presentation]. https://www.osti.gov/biblio/1645691 Publication ID: 70195
  • Bochev, P., Peterson, K., Kuberry, P., Trask, N., & Trask, N. (2019). Non-iterative partitioned methods based on monolithic formulations of the coupled problem [Conference Poster]. https://www.osti.gov/biblio/1641144 Publication ID: 69702
  • Perego, M., Bochev, P., Kuberry, P., Trask, N., & Trask, N. (2019). Generalized Moving Least Squares: Approximation Theory and Applications [Presentation]. https://www.osti.gov/biblio/1645573 Publication ID: 69710
  • Kuberry, P., Perego, M., Trask, N., Bochev, P., & Bochev, P. (2019). The Compadre Toolkit for Native Degrees-of-Freedom [Conference Poster]. https://www.osti.gov/biblio/1641034 Publication ID: 69548
  • Glusa, C. (2019). Asynchronous Domain Decomposition Solvers [Conference Poster]. https://www.osti.gov/biblio/1641087 Publication ID: 69620
  • Trask, N., Bochev, P., Perego, M., & Perego, M. (2019). Mimetic Conservation Principles for Meshfree Approximation [Conference Poster]. https://www.osti.gov/biblio/1640111 Publication ID: 68686
  • Bochev, P., Kuberry, P., Peterson, K., & Peterson, K. (2019). Explicit Partitioned Methods based on Monolithic Formulations of the Coupled Problem [Conference Poster]. https://www.osti.gov/biblio/1640129 Publication ID: 68717
  • Kuberry, P., Perego, M., Trask, N., Bochev, P., & Bochev, P. (2019). Field reconstruction from native degrees-of-freedom using the Compadre Toolkit [Conference Poster]. https://www.osti.gov/biblio/1640167 Publication ID: 68779
  • Perego, M., Bochev, P., Bosler, P., Kuberry, P., Peterson, K., Trask, N., & Trask, N. (2019). Advances in the Approximation Theory of Generalized Moving Least Squares [Conference Poster]. https://www.osti.gov/biblio/1640218 Publication ID: 68848
  • Peterson, K., Bochev, P., Kuberry, P., Trask, N., & Trask, N. (2019). Lagrange-Multiplier-Based Partitioned Method for Ocean-Atmosphere Coupling [Conference Poster]. https://www.osti.gov/biblio/1640221 Publication ID: 68854
  • Bochev, P., Trask, N., Kuberry, P., Perego, M., & Perego, M. (2019). Mesh-hardened finite element analysis through a Generalized Moving Least-Squares approximation of variational problems [Conference Poster]. https://doi.org/10.1007/978-3-030-41032-2_7 Publication ID: 68604
  • Perego, M., Bochev, P., Trask, N., Bosler, P., Kuberry, P., Peterson, K., & Peterson, K. (2019). Advances in the Approximation Theory for Generalized Moving Least Squares [Conference Poster]. https://www.osti.gov/biblio/1639699 Publication ID: 67960
  • Glusa, C. (2019). Asynchronous Domain Decomposition Solvers [Conference Poster]. https://www.osti.gov/biblio/1602126 Publication ID: 67113
  • Hu, J., Glusa, C., Lin, P., Phillips, E., Elliott, J., Siefert, C., Rajamanickam, S., & Rajamanickam, S. (2019). Large Scale Parallel Solution Methods for Electromagnetic Simulations [Conference Poster]. https://www.osti.gov/biblio/1602925 Publication ID: 67190
  • D’Elia, M., Bochev, P., Littlewood, D., Perego, M., & Perego, M. (2019). Optimization-based coupling of local and nonlocal models: Applications to Peridynamics. Handbook of Nonlocal Continuum Mechanics for Materials and Structures. https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85079581224&origin=inward Publication ID: 55462
  • Boman, E., Chow, E., Dongarra, J., Glusa, C., Rajamanickam, S., Szyld, D., Yamazaki, I., & Yamazaki, I. (2019). Asynchronous Iterative Solvers for Extreme Scale [Presentation]. https://www.osti.gov/biblio/1596422 Publication ID: 64517
  • Glusa, C., Ainsworth, M., & Ainsworth, M. (2019). Hybrid Finite Element – Spectral Method for the Spectral Fractional Laplacian [Conference Poster]. https://www.osti.gov/biblio/1593531 Publication ID: 64378
  • Berger-Vergiat, L., Glusa, C., Hu, J., Siefert, C., Tuminaro, R., Matthias, M., Andrey, P., Tobias, W., & Tobias, W. (2019). MueLu User’s Guide. https://doi.org/10.2172/1491860 Publication ID: 64392
  • Bochev, P. (2019). Optimization-based property-preserving methods [Conference Poster]. https://www.osti.gov/biblio/1595894 Publication ID: 64452
  • Kuberry, P., Bosler, P., Trask, N., Perego, M., Peterson, K., Bochev, P., & Bochev, P. (2018). The Compadre Toolkit [Conference Poster]. https://www.osti.gov/biblio/1594258 Publication ID: 59467
  • Glusa, C. (2018). RefMaxwell – MueLu’s Maxwell solver [Presentation]. https://www.osti.gov/biblio/1593000 Publication ID: 59789
  • Bochev, P., Trask, N., Kuberry, P., Perego, M., Peterson, K., Bosler, P., & Bosler, P. (2018). Compatible meshless methods for DPEs [Conference Poster]. https://www.osti.gov/biblio/1806965 Publication ID: 59543
  • Bettencourt, M.T., Kramer, R., Cartwright, K., Phillips, E., Ober, C., Pawlowski, R., Swan, M., Tezaur, I., Phipps, E., Conde, S., Cyr, E., Ulmer, C., Kordenbrock, T., Levy, S., Templet, G., Hu, J., Lin, P., Glusa, C., Siefert, C., Glass, M., & Glass, M. (2018). ASC ATDM Level 2 Milestone #6358: Assess Status of Next Generation Components and Physics Models in EMPIRE. https://doi.org/10.2172/1493832 Publication ID: 58868
  • Trask, N., Perego, M., Bochev, P., & Bochev, P. (2018). Discretely conservative meshfree schemes for conservation laws [Conference Poster]. https://www.osti.gov/biblio/1806699 Publication ID: 63328
  • Perego, M., Bochev, P., Trask, N., Bosler, P., Kuberry, P., Peterson, K., & Peterson, K. (2018). Advances in the Approximation Theory for Functional Reconstructions Using GMLS and Applications to Meshless Discretization of Differential Equations [Conference Poster]. https://www.osti.gov/biblio/1573545 Publication ID: 63442
  • Glusa, C. (2018). A Maxwell Solver for Next-Generation Platforms [Conference Poster]. https://www.osti.gov/biblio/1532820 Publication ID: 62953
  • Peterson, K., Bochev, P., Kuberry, P., & Kuberry, P. (2018). Explicit Partitioned Methods for Interface Coupling [Conference Poster]. https://www.osti.gov/biblio/1574283 Publication ID: 63478
  • Peterson, K., Bochev, P., Kuberry, P., & Kuberry, P. (2018). Explicit Partitioned Methods for Interface Coupling [Conference Poster]. https://www.osti.gov/biblio/1526419 Publication ID: 62555
  • Bochev, P., Perego, M., D’Elia, M., Ridzal, D., Peterson, K., & Peterson, K. (2018). Optimization-based property preserving finite element methods for transport equations [Conference Poster]. https://www.osti.gov/biblio/1525706 Publication ID: 62428
  • Kramer, R., Siefert, C., Voth, T., Bochev, P., & Bochev, P. (2018). Formulation and computation of dynamic, interface-compatible Whitney complexes in three dimensions. Journal of Computational Physics, 359, pp. 45-76. https://doi.org/10.1016/j.jcp.2017.12.037 Publication ID: 64073
  • Glusa, C. (2018). Asynchronous Domain Decomposition Solvers [Conference Poster]. https://www.osti.gov/biblio/1507816 Publication ID: 61256
  • Kuberry, P., Bochev, P., Peterson, K., & Peterson, K. (2018). Mesh-tying via multiple-control PDE-constrained optimization and GMLS function reconstruction [Conference Poster]. https://www.osti.gov/biblio/1504320 Publication ID: 61298
  • Bochev, P., Kuberry, P., Peterson, K., & Peterson, K. (2018). A virtual control coupling approach for problems with non-coincident discrete interfaces [Conference Poster]. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). https://doi.org/10.1007/978-3-319-73441-5_15 Publication ID: 56320
  • Ainsworth, M., Glusa, C., & Glusa, C. (2018). Hybrid finite element–spectral method for the fractional Laplacian: Approximation theory and efficient solver. SIAM Journal on Scientific Computing, 40(4), pp. A2383-A2405. https://doi.org/10.1137/17M1144696 Publication ID: 62261
  • Glusa, C., Ainsworth, M., & Ainsworth, M. (2018). The Resiliency of Multilevel Methods on Next Generation Computing Platforms: Probabilistic Model and Its Analysis [Conference Poster]. https://www.osti.gov/biblio/1573773 Publication ID: 58749
  • Hong, B.D., Perego, M., Bochev, P., Frischknecht, A., Phillips, E., & Phillips, E. (2018). Towards a scalable multifidelity simulation approach for electrokinetic problems at the mesoscale [Conference Poster]. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). https://doi.org/10.1007/978-3-319-73441-5_16 Publication ID: 56247
  • Peterson, K., Bochev, P., Trask, N., & Trask, N. (2018). Improving the Material-Point Method with GMLS [Presentation]. https://www.osti.gov/biblio/1512652 Publication ID: 58561
  • Glusa, C., Ainsworth, M., & Ainsworth, M. (2017). Adaptive FEM for the fractional Laplacian [Conference Poster]. https://www.osti.gov/biblio/1511974 Publication ID: 54654
  • Glusa, C., Ainsworth, M., & Ainsworth, M. (2017). Adaptive FEM for the fractional Laplacian [Conference Poster]. https://www.osti.gov/biblio/1573778 Publication ID: 54504
  • Cheung, J., Frischknecht, A., Perego, M., Bochev, P., & Bochev, P. (2017). A hybrid, coupled approach for modeling charged fluids from the nano to the mesoscale. Journal of Computational Physics, 348, pp. 364-384. https://doi.org/10.1016/j.jcp.2017.07.030 Publication ID: 48379
  • Kuberry, P., Bochev, P., Peterson, K., Phillips, E., & Phillips, E. (2017). Coupling Hyperbolic PDEs Over Non-Coincident Interfaces [Conference Poster]. https://www.osti.gov/biblio/1474028 Publication ID: 53073
  • Ridzal, D., D’Elia, M., Perego, M., Bochev, P., & Bochev, P. (2017). Property preserving finite element methods via constrained optimization [Conference Poster]. https://www.osti.gov/biblio/1513336 Publication ID: 53083
  • Trask, N., Bochev, P., Perego, M., & Perego, M. (2017). Locally compatible meshless methods for PDEs [Conference Poster]. https://www.osti.gov/biblio/1471967 Publication ID: 58532
  • Peterson, K., Ridzal, D., Bochev, P., & Bochev, P. (2017). Optimization-based Tracer Transport [Conference Poster]. https://www.osti.gov/biblio/1471980 Publication ID: 58536
  • Boman, E., Rajamanickam, S., Glusa, C., Chow, E., Ramanan, P., & Ramanan, P. (2017). Asynchronous Iterative Solvers: The ACHILES library and domain decomposition methods [Presentation]. https://www.osti.gov/biblio/1476153 Publication ID: 53246
  • Peterson, K., Bochev, P., Ridzal, D., Taylor, M., & Taylor, M. (2017). Optimization-Based Semi-Lagrangian Tracer Transport [Presentation]. https://www.osti.gov/biblio/1465013 Publication ID: 57961
  • Kuberry, P., Bochev, P., Peterson, K., Wong, M., & Wong, M. (2017). Bridging the gap: from algorithm development to mission impact a partitioned elastodynamics example [Conference Poster]. https://www.osti.gov/biblio/1465084 Publication ID: 57994
  • Glusa, C., Ainsworth, M., & Ainsworth, M. (2017). The Resiliency of Multilevel Methods on Next Generation Computing Platforms: Probabilistic Model and Its Analysis [Conference Poster]. https://www.osti.gov/biblio/1460163 Publication ID: 57172
  • Bochev, P. (2017). Optimization-Based Property Preserving Methods or going boldly beyond compatible discretizations [Conference Poster]. https://www.osti.gov/biblio/1513615 Publication ID: 57113
  • Peterson, K., Bochev, P., Kuberry, P., & Kuberry, P. (2017). Explicit Partitioned Methods for Coupled Problems Based on Lagrange Multipliers [Conference Poster]. https://www.osti.gov/biblio/1523700 Publication ID: 56903
  • Kuberry, P., Bochev, P., Peterson, K., & Peterson, K. (2017). An Optimization-Based Globally Flux-Conserving Coupling of Problems with Spatially Non-Coincident Interface Discretizations [Conference Poster]. https://www.osti.gov/biblio/1458183 Publication ID: 56697
  • Hong, B., Perego, M., Bochev, P., Frischknecht, A., Phillips, E., & Phillips, E. (2017). Towards a Scalable Multifidelity Simulation Approach for Electrokinetic Problems at the Mesoscale [Conference Poster]. https://doi.org/10.1007/978-3-319-73441-5_16 Publication ID: 56709
  • D’Elia, M., Bochev, P., D’Elia, M., Perego, M., Ridzal, D., & Ridzal, D. (2017). Optimization-based property preserving finite element methods [Conference Poster]. https://www.osti.gov/biblio/1458218 Publication ID: 56710
  • Bochev, P., Kuberry, P., Peterson, K., & Peterson, K. (2017). An explicit partitioned elastodynamics method based on Lagrange Multipliers [Conference Poster]. https://www.osti.gov/biblio/1458082 Publication ID: 56608
  • Peterson, K., Bochev, P., Perego, M., Gao, X., & Gao, X. (2017). Multiscale Stabilized Control Volume Finite Element Method for Advection-Diffusion [Conference Poster]. https://www.osti.gov/biblio/1456439 Publication ID: 55666
  • Peterson, K., Bochev, P., Kuberry, P., & Kuberry, P. (2017). Mortar Flux Recover (MFR) Algorithm and Analysis [Conference Poster]. https://www.osti.gov/biblio/1427961 Publication ID: 55378
  • Cheung, J., Frischknecht, A., Perego, M., Bochev, P., & Bochev, P. (2017). A Multifidelity Approach to Effectively Compute the Steady-State Flow Of Ionic Solutions [Conference Poster]. https://www.osti.gov/biblio/1429255 Publication ID: 55417
  • Kuberry, P., Bochev, P., Peterson, K., Phillips, E., & Phillips, E. (2017). A Partitioned Method for Explicit Elastodynamics Based on a Generalized Dual Schur Complement [Conference Poster]. https://www.osti.gov/biblio/1456371 Publication ID: 55505
  • D’Elia, M., Bochev, P., Perego, M., Littlewood, D., & Littlewood, D. (2017). Optimization based coupling for nonlocal and local models with applications to static peridynamics [Conference Poster]. https://www.osti.gov/biblio/1424841 Publication ID: 55060
  • Littlewood, D., D’Elia, M., Perego, M., Bochev, P., & Bochev, P. (2017). Optimization-Based Coupling for Local and Nonlocal Models [Conference Poster]. https://www.osti.gov/biblio/1424567 Publication ID: 55109
  • Kuberry, P., Bochev, P., Peterson, K., & Peterson, K. (2017). Optimization-Based Approach for Problems with Non-Conforming Interface Discretizations [Conference Poster]. https://www.osti.gov/biblio/1505690 Publication ID: 54110
  • Peterson, K., Bochev, P., Perego, M., Gao, X., & Gao, X. (2017). Stabilized Control Volume Finite Element Method for Drift Diffusion [Presentation]. https://www.osti.gov/biblio/1524972 Publication ID: 54429
  • Bochev, P., D’Elia, M., & D’Elia, M. (2017). Formulation and Analysis of a coupling strategy for nonlocal and local models [Conference Poster]. https://www.osti.gov/biblio/1505476 Publication ID: 53015
  • Trask, N., Perego, M., Bochev, P., & Bochev, P. (2017). A high-order staggered meshless method for elliptic problems. SIAM Journal on Scientific Computing, 39(2), pp. A479-A502. https://doi.org/10.1137/16M1055992 Publication ID: 46929
  • Peterson, K., Bochev, P., Kuberry, P., & Kuberry, P. (2016). Mortar Flux Recovery (MFR) Algorithm and Analysis [Conference Poster]. https://www.osti.gov/biblio/1400364 Publication ID: 47171
  • Frischknecht, A., Cheung, J., Hong, B., Perego, M., Bochev, P., & Bochev, P. (2016). Electrokinetic Models beyond Mean-Field Theory [Presentation]. https://www.osti.gov/biblio/1401931 Publication ID: 47208
  • Bochev, P. (2016). Advances in formula/on analysis and computa/on of concurrent coupling methods [Conference Poster]. https://www.osti.gov/biblio/1402328 Publication ID: 47236
  • Littlewood, D., D’Elia, M., Perego, M., Bochev, P., & Bochev, P. (2016). Optimization-Based Coupling for Local and Nonlocal Models [Conference Poster]. https://www.osti.gov/biblio/1390745 Publication ID: 52147
  • Kuberry, P., Bochev, P., Peterson, K., & Peterson, K. (2016). Explicit and Implicit Interface Coupling Approaches [Presentation]. https://www.osti.gov/biblio/1375103 Publication ID: 51582
  • D’Elia, M., Littlewood, D., Perego, M., Bochev, P., & Bochev, P. (2016). A COUPLING STRATEGY FOR LOCAL AND NONLOCAL MODELS with applications to static peridynamics [Conference Poster]. https://www.osti.gov/biblio/1373156 Publication ID: 51312
  • Bochev, P., Cheung, J., D’Elia, M., Frischknecht, A., Parks, M., Perego, M., & Perego, M. (2016). Coupling of Multi-fidelity Models: Applications to PNP-cDFT and local-nonlocal Poisson equations [Presentation]. https://www.osti.gov/biblio/1428032 Publication ID: 50761
  • D’Elia, M., Perego, M., Bochev, P., Littlewood, D., & Littlewood, D. (2016). A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions. Computers and Mathematics with Applications (Oxford), 71(11), pp. 2218-2230. https://doi.org/10.1016/j.camwa.2015.12.006 Publication ID: 45172
  • Gerritsma, M., Bochev, P., & Bochev, P. (2016). A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition. Computers and Mathematics with Applications, 71(11), pp. 2285-2300. https://doi.org/10.1016/j.camwa.2016.01.033 Publication ID: 45175
  • Bochev, P., Ridzal, D., & Ridzal, D. (2016). Optimization-based additive decomposition of weakly coercive problems with applications. Computers and Mathematics with Applications, 71(11), pp. 2140-2154. https://doi.org/10.1016/j.camwa.2015.12.032 Publication ID: 44430
  • D’Elia, M., Perego, M., Bochev, P., Littlewood, D., & Littlewood, D. (2016). A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions [Conference Poster]. Computers and Mathematics with Applications. https://doi.org/10.1016/j.camwa.2015.12.006 Publication ID: 46234
  • Kuberry, P., Bochev, P., & Bochev, P. (2016). An optimization-based approach to mesh tying and transmission problems [Conference Poster]. https://www.osti.gov/biblio/1368837 Publication ID: 50227
  • Kuberry, P., Bochev, P., & Bochev, P. (2016). An optimization-based approach to mesh tying and transmission problems [Conference Poster]. https://www.osti.gov/biblio/1422058 Publication ID: 48948
  • Bochev, P., Ridzal, D., & Ridzal, D. (2016). “Optimization-based additive decomposition of weakly coercive problems with applications to iterative solver design [Conference Poster]. https://www.osti.gov/biblio/1366604 Publication ID: 49131
  • Bochev, P. (2016). Optimization-based property preserving methods or going boldly beyond compatible discretization [Conference Poster]. https://www.osti.gov/biblio/1338867 Publication ID: 46592
  • Olson, D., Shapeev, A.V., Bochev, P., Luskin, M., & Luskin, M. (2016). Analysis of an optimization-based atomistic-to-continuum coupling method for point defects. ESAIM: Mathematical Modelling and Numerical Analysis, 50(1), pp. 1-41. https://doi.org/10.1137/13091734X Publication ID: 38888
  • D’Elia, M., Bochev, P., & Bochev, P. (2015). Heterogeneous Domain Decomposition methods for Nonlocal problems [Conference Poster]. https://www.osti.gov/biblio/1336014 Publication ID: 41857
  • Gao, X., Huang, A., Peterson, K., Hennigan, G., Musson, L., Bochev, P., & Bochev, P. (2015). Implementation of Different Stabilization Schemes in Charon Using Trilinos/Panzer [Conference Poster]. https://www.osti.gov/biblio/1331955 Publication ID: 46346
  • Perego, M., D’Elia, M., Bochev, P., Littlewood, D., & Littlewood, D. (2015). A coupling strategy for Local and Nonlocal continuum models [Conference Poster]. https://www.osti.gov/biblio/1336328 Publication ID: 45994
  • D’Elia, M., Perego, M., Bochev, P., Littlewood, D., & Littlewood, D. (2015). A coupling strategy for Local and Nonlocal continuum models [Conference Poster]. https://www.osti.gov/biblio/1289561 Publication ID: 44926
  • D’Elia, M., Bochev, P., & Bochev, P. (2015). Formulation Analysis and Computation of an Optimization-Based Local to Nonlocal coupling method [Conference Poster]. https://www.osti.gov/biblio/1289562 Publication ID: 44927
  • Perego, M., Price, S., Hoffman, M., Salinger, A., Bochev, P., Gunzburger, M., & Gunzburger, M. (2015). Coupling of Momentum Balance and Thickness Evolution Equations for Ice Sheet Modeling [Conference Poster]. https://www.osti.gov/biblio/1312674 Publication ID: 45244
  • Peterson, K., D’Elia, M., Ridzal, D., Bochev, P., Shashkov, M., & Shashkov, M. (2015). Optimization-based Mesh Correction [Conference Poster]. https://www.osti.gov/biblio/1326773 Publication ID: 45295
  • Bochev, P. (2015). Optimization-Based Property Preserving Methods or Going Boldly Beyond Compatible Discretizations [Presentation]. https://www.osti.gov/biblio/1331585 Publication ID: 44105
  • Bochev, P., D’Elia, M., & D’Elia, M. (2015). Optimization-based coupling of local and nonlocal continuum models: A divide and conquer approach for stable and physically consistent heterogeneous numerical models [Conference Poster]. https://www.osti.gov/biblio/1252913 Publication ID: 43341
  • D’Elia, M., Bochev, P., & Bochev, P. (2015). An Optimization-Based Local to Nonlocal Coupling Method [Conference Poster]. https://www.osti.gov/biblio/1253081 Publication ID: 43394
  • Bochev, P., Moe, S., Peterson, K., Ridzal, D., & Ridzal, D. (2015). A Conservative Optimization-based Semi-Lagrangian Spectral Element Method for Passive Tracer Transport [Conference Poster]. https://www.osti.gov/biblio/1253083 Publication ID: 43396
  • D’Elia, M., Bochev, P., & Bochev, P. (2015). An Optimization-Based coupling of Local and Nonlocal models [Presentation]. https://www.osti.gov/biblio/1253305 Publication ID: 43421
  • Bochev, P., Moe, S.A., Peterson, K., Ridzal, D., & Ridzal, D. (2015). A conservative, optimization-based semi-lagrangian spectral element method for passive tracer transport [Conference Poster]. COUPLED PROBLEMS 2015 – Proceedings of the 6th International Conference on Coupled Problems in Science and Engineering. https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84938700932&origin=inward Publication ID: 41486
  • Bochev, P., Kuberry, P., & Kuberry, P. (2015). A variational flux recovery approach for elastodynamics problems with interfaces [Conference Poster]. PANACM 2015 – 1st Pan-American Congress on Computational Mechanics, in conjunction with the 11th Argentine Congress on Computational Mechanics, MECOM 2015. https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84938717654&origin=inward Publication ID: 41511
  • Bochev, P., D’Elia, M., & D’Elia, M. (2015). An Optimization-Based Local to Nonlocal Coupling Method [Conference Poster]. https://www.osti.gov/biblio/1530976 Publication ID: 43050
  • Bochev, P., Kuberry, P., & Kuberry, P. (2015). A variational force recovery approach for elastodynamics problems with interfaces [Conference Poster]. https://www.osti.gov/biblio/1249293 Publication ID: 43163
  • Siefert, C., Kramer, R., Bochev, P., Voth, T., & Voth, T. (2015). Extended and Conformal Decomposition Finite Elements for 3D Compatible Discretizations [Conference Poster]. https://www.osti.gov/biblio/1241271 Publication ID: 42370
  • Bochev, P., Kuberry, P., & Kuberry, P. (2015). A new partitioned algorithm for explicit elastodynamics based on variational flux recovery [Conference Poster]. https://www.osti.gov/biblio/1882365 Publication ID: 42408
  • Peterson, K., Ridzal, D., Bochev, P., & Bochev, P. (2015). Feature-Preserving Finite Element Transport Across Interfaces: Part2, Direct Flux Recovery [Conference Poster]. https://www.osti.gov/biblio/1890367 Publication ID: 42426
  • Gerritsma, M., Bochev, P., & Bochev, P. (2015). A locally conservative high-order least-squares formulation in curvilinear coordinates [Conference Poster]. Lecture Notes in Computational Science and Engineering. https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84952042269&origin=inward Publication ID: 39037
  • D’Elia, M., Bochev, P., & Bochev, P. (2015). Optimization-based coupling of nonlocal and local diffusion models [Conference Poster]. Materials Research Society Symposium Proceedings. https://doi.org/10.1557/opl.2015.109 Publication ID: 39911
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May 9, 2023