Domain Decomposition Using a Schwarz Method

Ionut Danaila (), Pascal Joly, Sidi Mahmoud Kaber and Marie Postel
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Ionut Danaila: Université de Rouen Normandie, CNRS, Laboratoire de mathématiques Raphaël Salem
Pascal Joly: Laboratoire Jacques-Louis Lions
Sidi Mahmoud Kaber: Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions
Marie Postel: Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions

Chapter Chapter 10 in An Introduction to Scientific Computing, 2023, pp 221-245 from Springer

Abstract: Abstract Realistic modeling of physical problems often involves systems of partial differential equations (PDE), usually nonlinear, and is defined on domains that can have both a large size and a complex shape. In most cases, the selected numerical method requires that one discretize the domain, and the number of degrees of freedom can easily be more than what the available computer will handle. A simple answer to this technological lock is to subdivide the problem into smaller ones, that is, to compute the solution piecewise, as the solution of problems defined on subdomains of the initial one. Eventually, the global solution is the union of all the solutions of partial problems. The main difficulty arising in adopting this method is the definition of boundary conditions on each subdomain. In this chapter, we present the domain decomposition method with partial overlapping of the subdomains. One- and two- dimensional examples are treated. Their speed and memory performances are compared with standard single-domain finite-difference methods.

Date: 2023
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DOI: 10.1007/978-3-031-35032-0_10

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