On solution of large linear system : direct solver


In this seminar, three software packages to solve a large sparse linear system by direct method are reviewed, and usage of them on super-scalar parallel computer VCC, and vector parallel computer SX-ACE will be instructed as hands-on training.


- Overview of direct solver
- Data structure to store sparse matrix, CSR
- Usage of direct solver -- initialization, symbolic factorization, numeric factorization, forward/backward substitution, finalization
- How to link your code to one of those libraries on VCC/SX-ACE supercomputer.

Recommended to whom

- wants to solve large sparse linear system in a numerical simulation of fluid dynamics, structural analysis, or electromagnetic analysis
- is interested in parallel computation on shared memory architecture computer with multicore CPU
- has experience to write simulation code by C or Fortran


- This seminar consists of lecture and hands-on training. Please bring your own note PC, which can connect to network and with terminal software installed.
- A trial account of VCC/SX-ACE without a fee will be provided for this seminar.

About direct solver

In numerical simulation of fluid dynamics, structural analysis, or electromagnetic analysis, large linear and/or nonlinear systems, which are obtained by discretization process of partial differential equations, need to be solved. Nonlinear problem can be linearized by a Newton iteration, hence linear system with large sparse matrix should be treated.

There are two methods to solve sparse the matrix problem, direct method, e.g., LU-factorization and iterative method, e.g., conjugate gradient method. Direct solver can robustly find a solution of the linear system of matrix with large condition number, which is obtained from strong nonlinear problem or originated from phenomena with large jump of physical coefficients. Usually, these matrices are hard to solve by iterative methods. A drawback of direct solver is that it has large complexity of computation and consumes large memory. On the contrary, iterative method has lower complexity of computation but iterative process strongly depends on character of the matrix and it often does not converge in realistic time.

In this seminar, we deal with direct method, which recently achieves large progress in computational efficiency by parallelization thanks to advances in both two fields, software science, and mathematical theory. On VCC, super-scalar computer of Cybermedia Center, we can use Pardiso belonging to Intel MKL, and two open source software, MUMPS and Dissection. The later two packages also run on SX-ACE, vector computer. In the last part of this lecture, usage of three software packages is instructed as hands-on training. Since these direct solver can use multi-core CPU in shared memory computer, you can accelerate computational speed of your simulation code drastically. In addition, Dissection software has capability of computation by quadruple precision arithmetic, and then you can try to solve hard problems that are out of range of double precision arithmetic.


a presentation material(.pdf)
source codes for hands-on training(.tar.gz)

Date : October 18(Wednesday), 2017 13:30 - 16:00 (registration from 13:00)
Instructor: Cybermedia Center, Osaka University ( Lecturer : Dr. Atsushi Suzuki, Guest associate professor )
Venue: Cybermedia Commons, the first floor main hall at Cybermedia Center, Suita Campus
Type : classroom study and hands-on training
Quota: 30 persons (registration will be closed when number of participants exceeds 30)
Application deadline: October 16 (Monday), 2017 17:00

Reception has been closed.