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when we are working with an irregular domain in solution of PDEs using finite difference method, can we divide the irregular domain into several rectangular sub-domains and then solve the problem?

the boundary condition is known and when the firs sub-domain is solved, the obtained results are employed as boundary condition for the next sub-domain

This idea is similar to the numerical trapezoidal integration.

armin
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  • You can generally mesh an irregular domain with quadrilaterals. Each quad can then be mapped to a square, where finite differences can be used. You should note two things: (1) The mapping will introduce Jacobians in your equations (unless each quad already is a Cartesian rectangle), (2) Coupling the solution across the interfaces among the sub-domains is in general not as simple as you say. The stability of the finite difference implementation may be compromised unless the coupling is done properly. – ekkilop Oct 02 '17 at 08:12
  • You will want to do some "fusion" or coupling of the neighbouring domains. Sometimes you may want "overlap". It will be kind of an automatic transferred boundary condition reaching out letting the subdomains grab ahold of each other. – mathreadler Oct 02 '17 at 08:17
  • Thanks, the quads are Cartesian rectangles. How stability can be affected by coupling sub-domains? – armin Oct 02 '17 at 09:43

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