A Finite Difference Domain Decomposition Method Using Local Corrections for the Solution of Poisson's Equation

Balls, Gregory T.; Colella, Phillip

doi:10.1006/jcph.2002.7068

Cited by 39 publications

(25 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The computational cost of projection is not insignificant, and adds additional software complexity. We note, however, that recent work with Poisson solvers on adaptive grids ( [3,20]) have made this computational cost smaller than or comparable to that of the hyperbolic update.…”

Section: Discussionmentioning

confidence: 87%

An unsplit, cell-centered Godunov method for ideal MHD

Crockett

Colella

Fisher

et al. 2005

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

We present a second-order Godunov algorithm for multidimensional, ideal MHD. Our algorithm is based on the unsplit formulation of Colella (J. Comput. Phys. vol. 87, 1990), with all of the primary dependent variables centered at the same location. To properly represent the divergence-free condition of the magnetic fields, we apply a discrete projection to the intermediate values of the field at cell faces, and apply a filter to the primary dependent variables at the end of each time step. We test the method against a suite of linear and nonlinear tests to ascertain accuracy and stability of the scheme under a variety of conditions. The test suite includes rotated planar linear waves, MHD shock tube problems, low-beta flux tubes, and a magnetized rotor problem. For all of these cases, we observe that the algorithm is second-order accurate for smooth solutions, converges to the correct weak solution for problems involving shocks, and exhibits no evidence of instability or loss of accuracy due to the possible presence of non-solenoidal fields.

show abstract

Section: Discussionmentioning

confidence: 87%

An unsplit, cell-centered Godunov method for ideal MHD

Crockett

Colella

Fisher

et al. 2005

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…In addition, Yau developed a distributed matrix library that supports blocked-cyclic layouts and implemented Cannon's Matrix Multiplication algorithm and Cholesky and LU factorization (without pivoting). Balls and Colella built a 2D version of their Method of Local Corrections algorithm for solving the Poisson equation for constant coefficients over an infinite domain (PPS) [3]. Bonachea, Chapman and Putnam built a Microarray Optimal Oligo Selection Engine for selecting optimal oligonucleotide sequences from an entire genome of simple organisms, to be used in microarray design.…”

Section: Applicationsmentioning

confidence: 99%

Productivity and performance using partitioned global address space languages

Yelick

Bonachea

Chen

et al. 2007

Proceedings of the 2007 International Workshop on Parallel Symbolic Computation

Self Cite

128

View full text Add to dashboard Cite

Partitioned Global Address Space (PGAS) languages combine the programming convenience of shared memory with the locality and performance control of message passing. One such language, Unified Parallel C (UPC) is an extension of ISO C defined by a consortium that boasts multiple proprietary and open source compilers. Another PGAS language, Titanium, is a dialect of Java T M designed for high performance scientific computation. In this paper we describe some of the highlights of two related projects, the Titanium project centered at U.C. Berkeley and the UPC project centered at Lawrence Berkeley National Laboratory. Both compilers use a source-to-source strategy that translates the parallel languages to C with calls to a communication layer called GASNet. The result is portable highperformance compilers that run on a large variety of shared and distributed memory multiprocessors. Both projects combine compiler, runtime, and application efforts to demonstrate some of the performance and productivity advantages to these languages.

show abstract

“…In the second iteration, it only marks those that can complete by only calling methods that don't need to make any calls, or equivalently, those methods that can complete using only two stack frames. In general, a method is marked in the ith iteration if it can complete using i, and no less than i, stack frames 4 . As shown in the companion report, Algorithm 4.1 marks all methods that can complete using any number of stack frames [17].…”

Section: Bypass Edgesmentioning

confidence: 99%

Concurrency Analysis for Parallel Programs with Textually Aligned Barriers

Kamil

Yelick

2006

Languages and Compilers for Parallel Computing

View full text Add to dashboard Cite

Abstract.A fundamental problem in the analysis of parallel programs is to determine when two statements in a program may run concurrently. This analysis is the parallel analog to control flow analysis on serial programs and is useful in detecting parallel programming errors and as a precursor to semantics-preserving code transformations. We consider the problem of analyzing parallel programs that access shared memory and use barrier synchronization, specifically those with textually aligned barriers and single-valued expressions. We present an intermediate graph representation for parallel programs and an efficient interprocedural analysis algorithm that conservatively computes the set of all concurrent statements. We improve the precision of this algorithm by using context-free language reachability to ignore infeasible program paths. We then apply the algorithms to static race detection and show that it can benefit from the concurrency information provided.

show abstract

A Finite Difference Domain Decomposition Method Using Local Corrections for the Solution of Poisson's Equation

Cited by 39 publications

References 15 publications

An unsplit, cell-centered Godunov method for ideal MHD

An unsplit, cell-centered Godunov method for ideal MHD

Productivity and performance using partitioned global address space languages

Concurrency Analysis for Parallel Programs with Textually Aligned Barriers

Contact Info

Product

Resources

About