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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

URL: http://hdl.handle.net/10754/660105

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

Record Details Similar Records

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

APA (6^{th} 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 (16^{th} 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 17, 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 (7^{th} Edition):

Alharthi, Noha. “Fast High-order Integral Equation Solvers for Acoustic and Electromagnetic Scattering Problems.” 2019. Web. 17 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 17]. 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

Not specified: Masters Thesis or Doctoral Dissertation

King Abdullah University of Science and Technology

2. Sukkari, Dalal. High Performance Polar Decomposition on Manycore Systems and its application to Symmetric Eigensolvers and the Singular Value Decomposition.

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

URL: http://hdl.handle.net/10754/652466

The Polar Decomposition (PD) of a dense matrix is an important operation in linear algebra, while being a building block for solving the Symmetric Eigenvalue Problem (SEP) and computing the Singular Value Decomposition (SVD). It can be directly calculated through the SVD itself, or iteratively using the QR Dynamically-Weighted Halley (QDWH) algorithm. The former is difficult to parallelize due to the preponderant number of memory-bound operations during the bidiagonal reduction. The latter is an iterative method, which performs more floating-point operations than the SVD approach, but exposes at the same time more parallelism. Looking at the roadmap of the hardware technology scaling, algorithms perform- ing floating-point operations on locally cached data should be favored over those requiring expensive horizontal data movement. In this context, this thesis investigates new high-performance algorithmic designs of QDWH algorithm to compute the PD. Originally introduced by Nakatsukasa et al. [1, 2], our algorithmic contributions include mixed precision techniques, task-based formulations, and parallel asynchronous executions. Moreover, by making the PD competitive, its application to the SEP and the SVD becomes practical. In particular, we introduce for the first time new algorithms for partial SVD decomposition using QDWH. By the same token, we extend the QDWH to support partial eigen decomposition for SEP. We present new high-performance implementations of the QDWH-based algorithms relying on fine-grained computations, which allows exploiting the sparsity of the underlying data structure. To demonstrate performance efficiency, portability and scalability, we conduct benchmarking campaigns on some of the latest shared/distributed-memory systems. Our QDWH-based algorithm implementations outperform the state-of-the-art numerical libraries by up to 2.8x and 12x on shared and distributed-memory, respectively. The task-based QDWH has been integrated into the Chameleon library (https://gitlab.inria.fr/solverstack/chameleon) for support on shared-memory systems with hardware accelerators. It is also currently being used by astronomers from the Subaru telescope located at the summit of Mauna Kea, Hawaii, USA. The distributed-memory software library of QDWH and its SVD extension are freely available under modified-BSD license at https: //github.com/ecrc/qdwh.git and https://github.com/ecrc/ksvd.git, respectively. Both software libraries have been integrated into the Cray Scientific numerical library LibSci v17.11.1 and v19.02.1.
*Advisors/Committee Members: Keyes, David E. (advisor), Alouini, Mohamed-Slim (committee member), Laleg-Kirati, Taous-Meriem (committee member), Ltaief, Hatem (committee member), Kressner, Daniel (committee member).*

Subjects/Keywords: singular value decomposition; partial SVD; polar decompoisition; partial symetric Eigensolver; QDWH-based algorithm; Hight Performance Implementation

Record Details Similar Records

❌

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

APA (6^{th} Edition):

Sukkari, D. (2019). High Performance Polar Decomposition on Manycore Systems and its application to Symmetric Eigensolvers and the Singular Value Decomposition. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/652466

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Sukkari, Dalal. “High Performance Polar Decomposition on Manycore Systems and its application to Symmetric Eigensolvers and the Singular Value Decomposition.” 2019. Thesis, King Abdullah University of Science and Technology. Accessed April 17, 2021. http://hdl.handle.net/10754/652466.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Sukkari, Dalal. “High Performance Polar Decomposition on Manycore Systems and its application to Symmetric Eigensolvers and the Singular Value Decomposition.” 2019. Web. 17 Apr 2021.

Vancouver:

Sukkari D. High Performance Polar Decomposition on Manycore Systems and its application to Symmetric Eigensolvers and the Singular Value Decomposition. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2019. [cited 2021 Apr 17]. Available from: http://hdl.handle.net/10754/652466.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sukkari D. High Performance Polar Decomposition on Manycore Systems and its application to Symmetric Eigensolvers and the Singular Value Decomposition. [Thesis]. King Abdullah University of Science and Technology; 2019. Available from: http://hdl.handle.net/10754/652466

Not specified: Masters Thesis or Doctoral Dissertation