Grantee Research Project Results
1999 Progress Report: Partitioning Algorithms and Their Applications to Massively Parallel Computations of Multiphase Fluid Flows in Porous Media
EPA Grant Number: R825207Title: Partitioning Algorithms and Their Applications to Massively Parallel Computations of Multiphase Fluid Flows in Porous Media
Investigators: Ewing, Richard E. , Lazarov, Raytcho D. , Djidjev, Hristo , Vardi, Moshe
Current Investigators: Ewing, Richard E. , Djidjev, Hristo , Lazarov, Raytcho D. , Vardi, Moshe
Institution: Texas A & M University
Current Institution: Texas A & M University , Rice University
EPA Project Officer: Aja, Hayley
Project Period: November 1, 1996 through October 31, 1999
Project Period Covered by this Report: November 1, 1998 through October 31, 1999
Project Amount: $290,760
RFA: High Performance Computing (1996) RFA Text | Recipients Lists
Research Category: Human Health , Aquatic Ecosystems , Environmental Statistics
Objective:
During the third year of the grant, we have concentrated our efforts on the following interrelated groups of problems: (1) local error estimators and refinement strategies, (2) algorithms for partitioning and load balancing, (3) nonconforming domain decomposition methods and mortar approximations, (4) domain decomposition structure for parallel computations in fluid flow modeling, and (5) finite volume element methods for reactive flows in porous media.Progress Summary:
Local Error Estimators and Refinement Strategies. We have tested our two-dimensional code for adaptive grid refinement to the problem of flows in presence wells, and used the technique of multilevel grid refinement. We have experimentally studied applications of this code to the bioscreen problem (see our Web site at http://www.isc.tamu.edu/EPA/parallelcomp.html). We have concentrated our research on the problem of adaptive local grid refinement for three-dimensional problems, including design and implementation of a suitable data structure for parallel adaptive computations.Algorithms for Partitioning and Load Balancing. We have concentrated our efforts on implementation issues, working on two versions of our partitioning algorithms. The first implementation uses a simpler strategy for searching the graph based on the levels of a breadth-first search combined with recursive bisection. In addition, separators that give better ratio of component-to-boundary sizes were given higher priority than those that give a better balance. The second implementation is of an algorithm that exploits the planarity of the mesh and divides the graph directly into p parts, instead of recursively subdividing it.
Nonconforming Domain Decomposition Methods and Mortar Approximations. The finite volume approach has been combined with the technique of the finite element method in a new development that is very suitable for parallel groundwater simulations and mortar finite volume element (FVE) approximations. We have proposed numerical schemes using FVE on both the subdomains and on the interfaces.
Implementation of the Domain Decomposition Structure on Parallel Computers. Currently, we are running two-dimensional test problems on the bioscreen model with one concentration, and two-dimensional reservoirs with many wells. We also have investigated a new and very promising technique for domain decomposition computations using nonmatching grids and a multigrid technique for uniformly preconditioning linear systems arising from these approximations.
Finite Volume Element Methods for Reactive Flows in Porous Media. We have developed a general framework for obtaining finite volume element approximations and studying their error analysis, including linear elements and L-splines. All developed schemes are locally conservative and have optimal approximation properties in both two- and three-dimensional problems.
Future Activities:
The work initiated during the first 2 years will continue in the following areas:Local Error Estimators and Adaptive Grid Refinement. We plan to theoretically address problems of local refinement and well models, and implement these strategies in our codes. We plan to implement three-dimensional grid refinement algorithms based on the analysis of the singular behavior of the solution in the general framework of multilevel grid refinement. We also shall design and implement adaptive error estimates and the error indicators for designing adaptive strategies for finite volume element approximations based on posteriori error estimates. Our goal will be implementation of a fully automatic parallel adaptive grid refinement strategy for general grids.
Algorithms for Partitioning and Load Balancing. We plan to continue our implementation efforts by adding more algorithms and combining several strategies (e.g., multilevel partitioning, spectral partitioning, and Kernighan-Lin). We also will do some experimental work by running our algorithms on very large meshes and comparing the speed and the quality of the resulting partitions with those of other approaches. With regard to the problem of partitioning weighted graphs, we plan to continue our study on three-dimensional meshes.
Using Separators for Adaptive Mesh Partitioning. We plan to continue our ongoing work studying how the springs method works for smoothing three-dimensional meshes. Next, we will examine the more difficult problem of adapting the ideas for producing a new algorithm for mesh generation. We expect that such a generalization will not be straightforward, but believe there are useful properties of our approach that should be exploited further for the mesh generation problem.
Implementation of the Domain Decomposition Structure on Parallel Computers. Our goal for the last year is to have a running parallel code on Silicon Graphics Origin 2000 (with 16 processors) and to investigate various refinement strategies and methods for grid partitioning with load balancing. The results will be put together in optimal graph partitioning and grid refinement to study experimentally the performance of the method and for computer simulations of groundwater flow computations. Examples of such flows are bioscreens, water reservoirs, and petroleum reservoirs. Another step will be to consider mortar domain methods for gluing together approximations on nonmatching grids. Finally, we will explore and implement grid refinement strategies for three-dimensional problems, and highly efficient iterative techniques based on the BPS (Bramble, Pasciak, Schatz) and BEPS (Bramble, Ewing, Pasciak, Schatz)-like preconditioners will be implemented. We plan to apply these schemes to contaminant transport in groundwater reservoirs.
Finite Volume Approximations for Flow Problems. We will study finite volume methods of higher orders as well as finite volume methods of second order (or quadratic finite elements will be employed). This will lead to more accurate locally conservative approximations, and based on this new method and hierarchical presentation of the basis, we will develop a strategy of a posteriori error analysis and algorithms for grid refinement. We also will include strategies for adaptive grids to nonlocal in time transient problems. This class of methods is more expensive in terms of memory and adaptivity, so special consideration of the integral term will be needed, because the grid will change in time.
Journal Articles on this Report : 4 Displayed | Download in RIS Format
Other project views: | All 11 publications | 8 publications in selected types | All 4 journal articles |
---|
Type | Citation | ||
---|---|---|---|
|
Ewing RE, Lazarov RD. Finite volume element approximations of nonlocal in time one-dimensional plows in porous media. Computing 2000;64(2):157-182. |
R825207 (1999) R825207 (Final) |
not available |
|
Ewing R, Lazarov R, Lin YP. Finite volume element approximations of nonlocal reactive flows in porous media. Numerical Methods for Partial Differential Equations 2000;16(3):285-311. |
R825207 (1999) R825207 (Final) |
not available |
|
Gopalakrishnan J, Pasciak JE. Multigrid for the mortar finite element method. SIAM Journal on Numerical Analysis 2000, Volume: 37, Number: 3 (MAR 9), Page: 1029-1052. |
R825207 (1999) R825207 (Final) |
not available |
|
Lazarov RD, Pasciak JE, Vassilevski PS. Iterative solution of a coupled mixed and standard Galerkin discretization method for elliptic problems. Numerical Linear Algebra with Applications 2001;8(1):13-31. |
R825207 (1999) R825207 (Final) |
not available |
Supplemental Keywords:
supercomputing, modeling, parallel algorithms, porous media, fluid flow., RFA, Scientific Discipline, Ecosystem Protection/Environmental Exposure & Risk, Mathematics, computing technology, Environmental Monitoring, Environmental Engineering, adaptive grid model, ecosystem modeling, fate and transport, HPCC, computer science, multiphase fluid flows, data analysis, information technology, parallel computing, partitioning algorithmsRelevant Websites:
http://www.isc.tamu.edu/EPA/EPA.htmlProgress and Final Reports:
Original AbstractThe perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Conclusions drawn by the principal investigators have not been reviewed by the Agency.