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DOMAIN DECOMPOSITION & WALL LAWS(Domain Decomposition Methods and Related Topics)

open access: yesDOMAIN DECOMPOSITION & WALL LAWS(Domain Decomposition Methods and Related Topics)
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Domain decomposition method (DDM)

2023
This chapter concerns the use of domain decomposition (DD) methods for the surface integral equation (SIE)-based solution of time-harmonic electromagnetic wave problems. DD methods have attracted significant attention for solving partial differential equations.
Martin, Victor F.   +4 more
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PROJECTION DOMAIN DECOMPOSITION METHOD

Mathematical Models and Methods in Applied Sciences, 1994
A domain decomposition method using the projection approach is considered. The original elliptic problem is transformed to a set of analogous problems in subdomains and an abstract equation on the interface between subdomains, the latter being solved using Galerkin projection method with some special basis functions defined on the interface.
Agoshkov, V. I., Ovchinnikov, E.
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ADI method – Domain decomposition

Applied Numerical Mathematics, 2006
A domain decomposition algorithm which is based on an implicit prediction and fully implicit scheme for the interior values, for solving parabolic partial differential equations, is presented. It is shown that this algorithm without the correction procedure is unconditionally stable.
Jun, Younbae, Mai, Tsun-Zee
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Deep Domain Decomposition Methods: Helmholtz Equation

Advances in Applied Mathematics and Mechanics, 2023
Summary: This paper proposes a deep-learning-based Robin-Robin domain decomposition method (DeepDDM) for Helmholtz equations. We first present the plane wave activation-based neural network (PWNN), which is more efficient for solving Helmholtz equations with constant coefficients and wavenumber \(k\) than finite difference methods (FDM). On this basis,
Li, Wuyang   +4 more
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Some Nonoverlapping Domain Decomposition Methods

SIAM Review, 1998
The rough contents of the present paper are as follows: 1. Introduction. 2. Algebraic aspects of preconditioning techniques. 3. A model problem and outline. 4. Preliminaries of Sobolev spaces and finite element spaces. 5. Substructuring methods. 6. Neumann-Neumann methods. 7. Some other interface preconditioners. 8.
Xu, Jinchao, Zou, Jun
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The multipliers‐free domain decomposition methods

Numerical Methods for Partial Differential Equations, 2009
AbstractThis article concludes the development and summarizes a new approach to dual‐primal domain decomposition methods (DDM), generally referred to as “the multipliers‐free dual‐primal method.” Contrary to standard approaches, these new dual‐primal methods are formulated without recourse to Lagrange‐multipliers.
Herrera, Ismael, Yates, Robert A.
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