Iterative Methods for Elliptic Problems On Regions Partitioned Into Substructure

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Iterative Methods for Elliptic Problems On Regions Partitioned Into Substructure
Olof B Widlund
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The boundary r = Fh u fw, where r^ is the union of the two horizontal sides. Because of the simple geometry there are alternatives to equation (5. 2) when we search for problems wtiich, are eajy to solve. -Thus we can solve.
(5. 4) by separation of the variables; ''W^ido 'tMs by expanding in Fourier series in the horizontal directiDn:and ■sorvJng'the'>r^J11;i. Ng boundary value problems for a set of fourth order ordinary differential -equations. We note that the data for equa- tion (5. 4) is qu
...ite' special, bCit that we can always reduce our problem to this form by solving a preliminary separable problem. In the discrete case the appro- priate algorithmic' tools are the fafst Foi/rier transform and the Choleski algo- rithm for five diagonal linear systems of equations.
Equation (5. 4) can be used to define a mapping- from yqw to y]* on r, . To find a preconditioner, wer. 'consider another* sepafabl^ 'problem for which we can use a Fourier expansion in the vertical 'di rection. ' (5.


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