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An Invariant Embedding Approach to Domain Decomposition

Volzer, Joseph R
http://rave.ohiolink.edu/etdc/view?acc_num=case1396522159

Abstract Details

2014, Doctor of Philosophy, Case Western Reserve University, Applied Mathematics.
We consider the problem of numerically solving the wave scattering problem in two dimensions, when the scatterer consists of a sound-soft compact scatterer surrounded by a compactly supported scattering medium. The scattering problem in the exterior domain is solved using boundary integral equations, while the solution near the scatterer is best treated by finite element methods. It is well known that these solutions can be glued together using non-reflecting boundary conditions, a common choice being the Dirichlet-to-Neumman (Steklov-Poincare) map. If the support of the scattering medium is large, the interior problem may require a large mesh and become computationally intense. We consider an alternative method based on the idea of invariant imbedding: first numerically solve for the DtN map on a boundary of a small domain merely enclosing the sound-hard scatterer, and then radially propagate the map out of the support of the scattering medium. Special attention needs to be paid to the stability of the propagation scheme that requires a solution of a matrix-valued Riccati equation. It is shown that by applying an appropriate Cayley transform on the matrix, problems arising from resonances can be avoided.
Erkki Somersalo, PhD (Advisor)
Daniela Calvetti, PhD (Advisor)
Steven Izen, PhD (Committee Member)
Glenn Starkman, PhD (Committee Member)
201 p.
Mathematics
Invariant Embedding; Domain Decomposition; Dirichlet-to-Neumann map; Riccati Equations; Wave Scattering

Recommended Citations

Citations

  • Volzer, J. R. (2014). An Invariant Embedding Approach to Domain Decomposition [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1396522159

    APA Style (7th edition)

  • Volzer, Joseph. An Invariant Embedding Approach to Domain Decomposition. 2014. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1396522159.

    MLA Style (8th edition)

  • Volzer, Joseph. "An Invariant Embedding Approach to Domain Decomposition." Doctoral dissertation, Case Western Reserve University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=case1396522159

    Chicago Manual of Style (17th edition)

case1396522159
819
© 2014, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.