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Title A fast direct solver for boundary value problems with locally-perturbed geometries
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Publication Date
Date Accessioned
Degree MA
Discipline/Department Engineering
Degree Level masters
University/Publisher Rice University
Abstract Many problems in science and engineering can be formulated as integral equations with elliptic kernels. In particular, in optimal control and design problems, the domain geometry evolves and results in a sequence of discretized linear systems to be constructed and inverted. While the systems can be constructed and inverted independently, the computational cost is relatively high. In the case where the change in the domain geometry for each new problem is only local, i.e. the geometry remains the same except within a small subdomain, we are able to reduce the cost of inverting the new system by reusing the pre-computed fast direct solvers of the original system. The resulting solver only requires inexpensive matrix-vector multiplications and matrix inversion of small size, thus dramatically reducing the cost of inverting the new linear system.
Subjects/Keywords fast direct solvers; boundary integral equations; local perturbation
Contributors Gillman, Adrianna (advisor)
Language en
Country of Publication us
Record ID handle:1911/105467
Repository rice
Date Indexed 2021-04-14
Grantor Rice University
Issued Date 2017-05-17 00:00:00

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