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The addition of fields on different meshes

✍ Scribed by P.E. Farrell

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 814 KB
Volume: 230
Category: Article
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2011.01.028

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✦ Synopsis

Let T 1 and T 2 be two (arbitrarily unrelated) meshes of the same domain X & R d ; 1 6 d 6 3.

Let V 1 and V 2 be the discrete function spaces induced from these meshes by equipping them with some choice of basis functions. This work discusses the following problem: given two functions f 1 2 V f and f 2 2 V g , compute f 1 + f 2 . Despite the simple statement of the task, the general solution is not obvious, for the desired sum lies neither in V 1 nor in V 2 , and is not representable on either mesh. The problem is solved by efficiently constructing a supermesh T S of T 1 and T 2 which induces a superspace of both V 1 and V 2 . Once such a mesh is available, the desired quantity may be represented exactly (subject to roundoff).

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