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A FETI preconditioner for two dimensional edge element approximations of Maxwell equations on non matching grids

15 pages
A FETI PRECONDITIONER FOR TWO DIMENSIONAL EDGE ELEMENT APPROXIMATIONS OF MAXWELL'S EQUATIONS ON NON-MATCHING GRIDS FRANCESCA RAPETTI AND ANDREA TOSELLI y Abstract. A class of FETI methods for the mortar approximation of a vector eld problem in two dimensions is introduced and analyzed. Edge element discretizations of lowest degree are con- sidered. The method proposed can be employed with geometrically conforming and non{conforming partitions. Our numerical results show that its condition number increases only with the number of unknowns in each subdomains, and is independent of the number of subdomains and the size of the problem. Key words. Edge elements, Maxwell's equations, domain decomposition, FETI, precondition- ers, non-matching grids AMS subject classications. 65F10, 65N22, 65N30, 65N55 1. Introduction. In this paper, we consider the boundary value problem Lu := curl (a curlu) +A u = f in ; u t = 0 on @ ; (1) with a bounded polygonal domain in R 2 . Here curl v := 2 6 6 4 @v @x 2 @v @x 1 3 7 7 5 ; curlu := @u 2 @x 1 @u 1 @x 2 ; see, e.

  • approximation

  • dimensional subspace

  • then eliminated

  • dependent problems

  • can then

  • mortar approximations

  • sciences program

  • applied mathematical

  • feti


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2
7
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cal
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k
k
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i
h
b
i
e
B
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:=
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function
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ciated
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to
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h
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see
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write
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.

W
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tro
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t
cal
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forms
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matrices
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t
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as
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r
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mortar
J
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m

;
u
where
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on

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metho
constrain
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B
for
=
the
solution

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