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Finite element solution of optimal control problems arising in semiconductor modeling

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Bochev, Pavel B.; Ridzal, Denis

Optimal design, parameter estimation, and inverse problems arising in the modeling of semiconductor devices lead to optimization problems constrained by systems of PDEs. We study the impact of different state equation discretizations on optimization problems whose objective functionals involve flux terms. Galerkin methods, in which the flux is a derived quantity, are compared with mixed Galerkin discretizations where the flux is approximated directly. Our results show that the latter approach leads to more robust and accurate solutions of the optimization problem, especially for highly heterogeneous materials with large jumps in material properties. © 2008 Springer.

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TYPE Conference YEAR 2008
OSTIScopus

A mathematical framework for multiscale science and engineering : the variational multiscale method and interscale transfer operators

Bochev, Pavel B.; Collis, Samuel S.; Jones, Reese E.; Lehoucq, Rich; Parks, Michael L.; Scovazzi, Guglielmo S.; Silling, Stewart; Templeton, J.A.; Wagner, Gregory J.

This report is a collection of documents written as part of the Laboratory Directed Research and Development (LDRD) project A Mathematical Framework for Multiscale Science and Engineering: The Variational Multiscale Method and Interscale Transfer Operators. We present developments in two categories of multiscale mathematics and analysis. The first, continuum-to-continuum (CtC) multiscale, includes problems that allow application of the same continuum model at all scales with the primary barrier to simulation being computing resources. The second, atomistic-to-continuum (AtC) multiscale, represents applications where detailed physics at the atomistic or molecular level must be simulated to resolve the small scales, but the effect on and coupling to the continuum level is frequently unclear.

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TYPE SAND Report YEAR 2007
DOIOSTI

Stabilization of low-order mixed finite elements for the stokes equations

SIAM Journal on Numerical Analysis

Bochev, Pavel B.; Dohrmann, Clark R.; Gunzburger, Max D.

We present a new family of stabilized methods for the Stokes problem. The focus of the paper is on the lowest order velocity-pressure pairs. While not LBB compliant, their simplicity and attractive computational properties make these pairs a popular choice in engineering practice. Our stabilization approach is motivated by terms that characterize the LBB "deficiency" of the unstable spaces. The stabilized methods are defined by using these terms to modify the saddle-point Lagrangian associated with the Stokes equations. The new stabilized methods offer a number of attractive computational properties. In contrast to other stabilization procedures, they are parameter free, do not require calculation of higher order derivatives or edge-based data structures, and always lead to symmetric linear systems. Furthermore, the new methods are unconditionally stable, achieve optimal accuracy with respect to solution regularity, and have simple and straightforward implementations. We present numerical results in two and three dimensions that showcase the excellent stability and accuracy of the new methods. © 2006 Society for Industrial and Applied Mathematics.

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TYPE Journal Article YEAR 2006
ScopusOSTI
Results 201–225 of 245
Results 201–225 of 245