Iterative Methods for Elliptic Problems On Regions Partitioned Into Substructure
Iterative Methods for Elliptic Problems On Regions Partitioned Into Substructure
Olof B Widlund
The book Iterative Methods for Elliptic Problems On Regions Partitioned Into Substructure was written by author Olof B Widlund Here you can read free online of Iterative Methods for Elliptic Problems On Regions Partitioned Into Substructure book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Iterative Methods for Elliptic Problems On Regions Partitioned Into Substructure a good or bad book?
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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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