论文信息 - Optimized Domain Decomposition Methods for the Spherical Laplacian

Optimized Domain Decomposition Methods for the Spherical Laplacian

The Schwarz iteration decomposes a boundary value problem over a large domain $\Omega$ into smaller subproblems by iteratively solving Dirichlet problems on a cover $\Omega_{1},\dots,\Omega_{p}$ of $\Omega$. In this paper, we discuss alternate transmission conditions that lead to faster convergence for the Laplacian on the sphere $\Omega$. We look at Robin conditions, second order tangential conditions, and a discretized version of an optimal but nonlocal operator.

[1] Frédéric Nataf,et al. Improved interface conditions for a non-overlapping domain decomposition of a non-convex polygonal domain , 2006 .

[2] Jun Mu. Solving the Laplace-Beltrami equation onS2 using spherical triangles , 1996 .

[3] Jung-Han Kimn,et al. A convergence theory for an overlapping Schwarz algorithm using discontinuous iterates , 2005, Numerische Mathematik.

[4] Gert Lube,et al. A Non-Overlapping Domain Decomposition Method for the Advection-Diffusion Problem , 1999, Computing.

[5] Qingping Deng. An Optimal Parallel Nonoverlapping Domain Decomposition Iterative Procedure , 2003, SIAM J. Numer. Anal..

[6] Frédéric Nataf,et al. Convergence rate of some domain decomposition methods for overlapping and nonoverlapping subdomains , 1997 .

[7] Charles M. Elliott,et al. Finite elements on evolving surfaces , 2007 .

[8] Frédéric Nataf,et al. Symmetrized Method with Optimized Second-Order Conditions for the Helmholtz Equation , 1998 .

[9] Alan Demlow,et al. An Adaptive Finite Element Method for the Laplace-Beltrami Operator on Implicitly Defined Surfaces , 2007, SIAM J. Numer. Anal..

[10] M. Gander,et al. Absorbing boundary conditions for the wave equation and parallel computing , 2004, Math. Comput..

[11] A. Staniforth,et al. Semi-Lagrangian integration schemes for atmospheric models - A review , 1991 .