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日時:2013 年 9 月 25 日(水)17:30 ~ 18:30(懇親会:19:00 ~)
場所:東京大学 情報基盤センター(浅野地区)4階遠隔会議室(地図
主催:東京大学情報基盤センター スーパーコンピューティング部門



14th Advanced Supercomputing Environment (ASE) Seminar

September 25th (Wednesday), 2013

Information Technology Center (Asano Section), The University of Tokyo
4F Telecommunication Meeting Room


Invited Speaker

Professor Weichung Wang
Institute of Applied Mathematical Sciences National Taiwan University


Solving Large-scale Eigenvalue Problems on Multicore CPU and GPU for 3D Photonic Crystal Simulations


Three-dimensional photonic crystals can be modeled by the Maxwell equations as generalized eigenvalue problems (GEVP). Numerical solutions of the resulting discretized large-scale GEVP play an important role to reveal physical properties and to boost innovative applications of photonic crystals. However, to solve these eigenvalue problems remains a computational challenge in both timing and accuracy because there are many unwanted zero eigenvalues, the coefficient matrix is complicated, and the problem size is large. We tackle this challenge by several novel and efficient matrix computation schemes. The main tool is the explicit eigendecomposition of the degenerate coefficient matrix. By using the explicit eigendecomposition, we transfer the GEVP to a standard eigenvalue problem (SEVP) that contains only the positive eigenvalues and the size is two-third of the original GEVP. The SEVP can be solved by inverse Lanczos method containing several efficient features. (i) The embed linear systems are well-conditioned and can be solved by Conjugate Gradient method without preconditioning. (ii) The most computational costly parts can be rewritten as FFT. (iii) The algorithms are suitable for parallel computers. We implement the algorithms on both multicore CPU and GPU. Numerical experiments show that the proposed eigenvalue solver is very efficient for various geometric structure of the photonic crystals.

19:00- Reception near Hongo

Financial supports:

* Grant-in-Aid for Scientific Research (A), "Research on Software Foundations for General Purpose Automatic Tuning Mechanisms"

* Grant-in-Aid for Scientific Research (B), "Exa-scale Adaptation to Sparse Iterative Library with Run-time Auto-tuning Facility"

* JST CREST, "An Evolutionary Approach to Construction of a Software Development Environment for Massively-Parallel Heterogeneous Systems"

( 9月17日(火)12時までに、katagiri@cc.u-tokyo.ac.jpまで送付 )

 日時:2013 年 9 月 25 日(水)19:00 ~
 予算:5,000 円程度


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