Publications

Abstract not provided.

We formulate and analyze an optimization-based Atomistic-to-Continuum (AtC) coupling method for problems with point defects. Application of a potential-based atomistic model near the defect core enables accurate simulation of the defect. Away from the core, where site energies become nearly independent of the lattice position, the method switches to a more efficient continuum model. The two models are merged by minimizing the mismatch of their states on an overlap region, subject to the atomistic and continuum force balance equations acting independently in their domains. We prove that the optimization problem is well-posed and establish error estimates.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

We present a new explicit algorithm for linear elastodynamic problems with material interfaces. The method discretizes the governing equations independently on each material subdomain and then connects them by exchanging forces and masses across the material interface. Variational flux recovery techniques provide the force and mass approximations. The new algorithm has attractive computational properties. It allows different discretizations on each material subdomain and enables partitioned solution of the discretized equations. The method passes a linear patch test and recovers the solution of a monolithic discretization of the governing equations when interface grids match.

We present a new optimization-based, conservative, and quasi-monotone method for passive tracer transport. The scheme combines high-order spectral element discretization in space with semi-Lagrangian time stepping. Solution of a singly linearly constrained quadratic program with simple bounds enforces conservation and physically motivated solution bounds. The scheme can handle efficiently a large number of passive tracers because the semi-Lagrangian time stepping only needs to evolve the grid points where the primitive variables are stored and allows for larger time steps than a conventional explicit spectral element method. Numerical examples show that the use of optimization to enforce physical properties does not affect significantly the spectral accuracy for smooth solutions. Performance studies reveal the benefits of high-order approximations, including for discontinuous solutions.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are also satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.

Abstract not provided.

Abstract not provided.

Abstract not provided.