A Parallel Method for Tridiagonal Equations

Wang, H. H.

doi:10.1145/355945.355947

Cited by 245 publications

(94 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The time t,, is smaller than the computing time 20An + lOAm + 6Cm of Kowalik's algorithm (1984). Also the algorithm of Wang (1981) requires more operations than ours. Bondeli (1991) does not give the computing time for parallel systems.…”

Section: The Algorithm For Other Boundary Conditionsmentioning

confidence: 92%

See 1 more Smart Citation

Parallel solution of tridiagonal systems for the Poisson equation

Schumann¹,

Strietzel²

1995

J Sci Comput

View full text Add to dashboard Cite

A method is described to solve the systems of tridiagonal linear equations that result from discrete approximations of the Poisson or Helmholtz equation with either periodic, Dirichlet, Neumann, or shear-periodic boundary conditions. The problem is partitioned into a set of smaller Dirichlet problems which can be solved simultaneously on parallel or vector computers leaving a smaller tridiagonal system to be solved on one of the processors,

show abstract

Section: The Algorithm For Other Boundary Conditionsmentioning

confidence: 92%

“…The method to be described in this paper is similar to the partition method derived by Wang (1981) for diagonally dominant tridiagonal systems with variable coefficients. He divides the matrix of the linear system into blocks and first eliminates the unknowns from the block's interior by a suitable Gaussian elimination procedure.…”

mentioning

confidence: 99%

Parallel solution of tridiagonal systems for the Poisson equation

Schumann¹,

Strietzel²

1995

J Sci Comput

View full text Add to dashboard Cite

show abstract

“…= P ! ), because the algorithm, whether it is Partitioned Thomas method [7] or odd--even cyclic reduction [6], is easily applicable to a 1--D processor grid, and the usual block size n ! is much smaller than the number of blocks n !…”

Section: Selection Of the Parallel Algorithmmentioning

confidence: 99%

“…subsystem, which proceeds with eliminations by the Thomas method simultaneously and results in "fill--in" blocks. The "fill--in" blocks are managed to find a solution through the communications between the subsystems [7]. Conversely, the cyclic odd--even reduction algorithm [6] has no matrix fill--in step that requires significant additional time in the partitioned Thomas method.…”

Section: Selection Of the Parallel Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

A block-tridiagonal solver with two-level parallelization for finite element-spectral codes

Lee¹,

Wright²

2014

Computer Physics Communications

View full text Add to dashboard Cite

Abstract:Two--level parallelization is introduced to solve a massive block--tridiagonal matrix system. One--level is used for distributing blocks whose size is as large as the number of block rows due to the spectral basis, and the other level is used for parallelizing in the block row dimension. The purpose of the added parallelization dimension is to retard the saturation of the scaling due to communication overhead and inefficiencies in the single--level parallelization only distributing blocks. As a technique for parallelizing the tridiagonal matrix, the combined method of "Partitioned Thomas method" and "Cyclic Odd--Even Reduction" is implemented in an MPI--Fortran90 based finite element--spectral code (TORIC) that calculates the propagation of electromagnetic waves in a tokamak. The two--level parallel solver using thousands of processors shows more than 5 times improved computation speed with the optimized processor grid compared to the single--level parallel solver under the same conditions. Three--dimensional RF field reconstructions in a tokamak are shown as examples of the physics simulations that have been enabled by this algorithmic advance.

show abstract

Performance comparison of a set of periodic and non-periodic tridiagonal solvers on SP2 and Paragon parallel computers

Sun

Moitra

1997

Concurrency: Pract. Exper.

View full text Add to dashboard Cite

Various tridiagonal solvers have been proposed in recent years for different parallel platforms. In this paper, the performance of three tridiagonal solvers, namely, the parallel partition LU algorithm, the parallel diagonal dominant algorithm, and the reduced diagonal dominant algorithm, is studied. These algorithms are designed for distributed‐memory machines and are tested on an Intel Paragon and an IBM SP2 machine. Measured results are reported in terms of execution time and speedup. Analytical studies are conducted for different communication topologies and for different tridiagonal systems. The measured results match the analytical results closely. In addition to addressing implementation issues, performance considerations such as problem sizes and models of speedup are also discussed. © 1997 John Wiley & Sons, Ltd.

show abstract

A Parallel Method for Tridiagonal Equations

Cited by 245 publications

References 6 publications

Parallel solution of tridiagonal systems for the Poisson equation

Parallel solution of tridiagonal systems for the Poisson equation

A block-tridiagonal solver with two-level parallelization for finite element-spectral codes

Performance comparison of a set of periodic and non-periodic tridiagonal solvers on SP2 and Paragon parallel computers

Contact Info

Product

Resources

About