Marcus J. Grote

Exact nonreflecting boundary condition for elastic waves

An exact nonreflecting boundary condition is derived for the time-dependent elastic wave equation in three space dimensions. This condition holds on a spherical surface

Robust Parallel Smoothing for Multigrid Via Sparse Approximate Inverses

\mathcal B

Sparse approximate inverse smoothers for geometric and algebraic multigrid

, outside of which the medium is assumed to be linear, homogeneous, isotropic, and source-free. It is local in time, nonlocal on

Non‐reflecting boundary conditions for electromagnetic scattering

\mathcal B

Meta-stability of equilibrium statistical structures for prototype geophysical flows with damping and driving

, and involves only first derivatives of the solution. Therefore it can be combined easily with any numerical method in the interior region.

Crude closure for flow with topography through large-scale statistical theory

Sparse approximate inverses are considered as smoothers for multigrid. They are based on the SPAI-Algorithm [M. J. Grote and T. Huckle, SIAM J. Sci. Comput., 18 (1997), pp. 838--853], which constructs a sparse approximate inverse M of a matrix A by minimizing I -MA in the Frobenius norm. This yields a new hierarchy of smoothers: SPAI-0, SPAI-1, SPAI

Analytical Models for Vertical Collapse and Instability in Stably Stratified Flows

(\varepsilon)

Nonreflecting Boundary Conditions for Elastodynamic Scattering

. Advantages of SPAI smoothers over classical smoothers are inherent parallelism, possible local adaptivity, and improved robustness. The simplest smoother, SPAI-0, is based on a diagonal matrix M. It is shown to satisfy the smoothing property for symmetric positive definite problems. Numerical experiments show that SPAI-0 smoothing is usually preferable to damped Jacobi smoothing. For the SPAI-1 smoother the sparsity pattern of M is that of A; its performance is typically comparable to that of Gauss--Seidel smoothing; however, both the computation and the application of the smoother remain inherently parallel. In more difficult situations, where the simpler SPAI-0 and SPAI-1 smoothers are not adequate, the SPAI

Robust parallel smoothing for multigrid via sparse approximate inverses

(\varepsilon)

The fluctuation-dissipation theorem for complex nonlinear systems

smoother provides a natural procedure for improvement where needed. Numerical examples illustrate the usefulness of SPAI smoothing.