# Massively parallel fast elliptic equation solver for three dimensional hydrodynamics and relativity

## Abstract

Through the work proposed in this document we expect to advance the forefront of large scale computational efforts on massively parallel distributed-memory multiprocessors. We will develop tools for effective conversion to a parallel implementation of sequential numerical methods used to solve large systems of partial differential equations. The research supported by this work will involve conversion of a program which does state of the art modeling of multi-dimensional hydrodynamics, general relativity and particle transport in energetic astrophysical environments. The proposed parallel algorithm development, particularly the study and development of fast elliptic equation solvers, could significantly benefit this program and other applications involving solutions to systems of differential equations. We shall develop a data communication manager for distributed memory computers as an aid in program conversions to a parallel environment and implement it in the three dimensional relativistic hydrodynamics program discussed below; develop a concurrent system/concurrent subgrid multigrid method. Currently, five systems are approximated sequentially using multigrid successive overrelaxation. Results from an iteration cycle of one multigrid system are used in following multigrid systems iterations. We shall develop a multigrid algorithm for simultaneous computation of the sets of equations. In addition, we shall implement a method for concurrent processing of themore »

- Authors:

- Lawrence Livermore National Lab., CA (United States)
- San Jose State Univ., CA (United States). Dept. of Mathematics and Computer Science

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab., CA (United States)

- Sponsoring Org.:
- USDOE, Washington, DC (United States)

- OSTI Identifier:
- 34202

- Report Number(s):
- UCRL-ID-119803

ON: DE95009385

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: Jan 1995

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; PARTIAL DIFFERENTIAL EQUATIONS; PARALLEL PROCESSING; NUMERICAL SOLUTION; ARRAY PROCESSORS; THREE-DIMENSIONAL CALCULATIONS; DISTRIBUTED DATA PROCESSING; RELATIVITY THEORY; ALGORITHMS; ITERATIVE METHODS; ELLIPTICAL CONFIGURATION; NEUTRON STARS

### Citation Formats

```
Sholl, P.L., Wilson, J.R., Mathews, G.J., and Avila, J.H.
```*Massively parallel fast elliptic equation solver for three dimensional hydrodynamics and relativity*. United States: N. p., 1995.
Web. doi:10.2172/34202.

```
Sholl, P.L., Wilson, J.R., Mathews, G.J., & Avila, J.H.
```*Massively parallel fast elliptic equation solver for three dimensional hydrodynamics and relativity*. United States. doi:10.2172/34202.

```
Sholl, P.L., Wilson, J.R., Mathews, G.J., and Avila, J.H. Sun .
"Massively parallel fast elliptic equation solver for three dimensional hydrodynamics and relativity". United States.
doi:10.2172/34202. https://www.osti.gov/servlets/purl/34202.
```

```
@article{osti_34202,
```

title = {Massively parallel fast elliptic equation solver for three dimensional hydrodynamics and relativity},

author = {Sholl, P.L. and Wilson, J.R. and Mathews, G.J. and Avila, J.H.},

abstractNote = {Through the work proposed in this document we expect to advance the forefront of large scale computational efforts on massively parallel distributed-memory multiprocessors. We will develop tools for effective conversion to a parallel implementation of sequential numerical methods used to solve large systems of partial differential equations. The research supported by this work will involve conversion of a program which does state of the art modeling of multi-dimensional hydrodynamics, general relativity and particle transport in energetic astrophysical environments. The proposed parallel algorithm development, particularly the study and development of fast elliptic equation solvers, could significantly benefit this program and other applications involving solutions to systems of differential equations. We shall develop a data communication manager for distributed memory computers as an aid in program conversions to a parallel environment and implement it in the three dimensional relativistic hydrodynamics program discussed below; develop a concurrent system/concurrent subgrid multigrid method. Currently, five systems are approximated sequentially using multigrid successive overrelaxation. Results from an iteration cycle of one multigrid system are used in following multigrid systems iterations. We shall develop a multigrid algorithm for simultaneous computation of the sets of equations. In addition, we shall implement a method for concurrent processing of the subgrids in each of the multigrid computations. The conditions for convergence of the method will be examined. We`ll compare this technique to other parallel multigrid techniques, such as distributed data/sequential subgrids and the Parallel Superconvergent Multigrid of Frederickson and McBryan. We expect the results of these studies to offer insight and tools both for the selection of new algorithms as well as for conversion of existing large codes for massively parallel architectures.},

doi = {10.2172/34202},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sun Jan 01 00:00:00 EST 1995},

month = {Sun Jan 01 00:00:00 EST 1995}

}