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King Abdullah University of Science and Technology

1. Alharthi, Noha. Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2019, King Abdullah University of Science and Technology

Acoustic and electromagnetic scattering from arbitrarily shaped structures can be numerically characterized by solving various surface integral equations (SIEs). One of the most effective techniques to solve SIEs is the Nyström method. Compared to other existing methods,the Nyström method is easier to implement especially when the geometrical discretization is non-conforming and higher-order representations of the geometry and unknowns are desired. However,singularities of the Green’s function are more difficult to”manage”since they are not ”smoothened” through the use of a testing function. This dissertation describes purely numerical schemes to account for different orders of singularities that appear in acoustic and electromagnetic SIEs when they are solved by a high-order Nyström method utilizing a mesh of curved discretization elements. These schemes make use of two sets of basis functions to smoothen singular integrals: the grid robust high-order Lagrange and the high-order Silvester-Lagrange interpolation basis functions. Numerical results comparing the convergence of two schemes are presented. Moreover, an extremely scalable implementation of fast multipole method (FMM) is developed to efficiently (and iteratively) solve the linear system resulting from the discretization of the acoustic SIEs by the Nyström method. The implementation results in O(N log N) complexity for high-frequency scattering problems. This FMM-accelerated solver can handle N =2 billion on a 200,000-core Cray XC40 with 85% strong scaling efficiency. Iterative solvers are often ineffective for ill-conditioned problems. Thus, a fast direct (LU)solver,which makes use of low-rank matrix approximations,is also developed. This solver relies on tile low rank (TLR) data compression format, as implemented in the hierarchical computations on many corearchitectures (HiCMA) library. This requires to taskify the underlying SIE kernels to expose fine-grained computations. The resulting asynchronous execution permit to weaken the artifactual synchronization points,while mitigating the overhead of data motion. We compare the obtained performance results of our TLRLU factorization against the state-of-the-art dense factorizations on shared memory systems. We achieve up to a fourfold performance speedup on a 3D acoustic problem with up to 150 K unknowns in double complex precision arithmetics. Advisors/Committee Members: Keyes, David E. (advisor), Hadwiger, Markus (committee member), Bagci, Hakan (committee member), Kressner, Daniel (committee member).

Subjects/Keywords: Boundary Integral Equation; Acoustic Scattering; LU-Based Solver; Fast Solvers; Fast Multipole Solvers; Tile Low-Rank Approximations

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Alharthi, N. (2019). Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/660105

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Alharthi, Noha. “Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems.” 2019. Thesis, King Abdullah University of Science and Technology. Accessed April 21, 2021. http://hdl.handle.net/10754/660105.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Alharthi, Noha. “Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems.” 2019. Web. 21 Apr 2021.

Vancouver:

Alharthi N. Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2019. [cited 2021 Apr 21]. Available from: http://hdl.handle.net/10754/660105.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Alharthi N. Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems. [Thesis]. King Abdullah University of Science and Technology; 2019. Available from: http://hdl.handle.net/10754/660105

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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