SparSol is a software package intended for preconditioned iterative solution of large sparse linear systems. It includes a number of iterative methods, preconditioners, scaling and reordering algorithms allowing one to choose the optimal combination of algorithms for a particular problem. The paper briefly describes the implemented algorithms and numerically compares the performance of SparSol with that of several popular, freely available software packages using test systems arising from hydrocarbon reservoir simulations.
Numerical simulation of reservoirs is an integral part of geoscientific studies to optimize petroleum recovery. Modern petroleum reservoir simulation requires simulating detailed and computationally expensive geological and physical models. Parallel reservoir simulators have the potential to solve larger, more realistic problems than previously possible.
To make the solution of these large problems feasible, an efficient parallel implementation of the algorithm is necessary. Such a parallelization of the algorithm requires proper data structures and data layout, some parallel direct and iterative solvers, and some parallel preconditioners. For the development of parallel reservoir simulator, we found the Trilinos Project to be an efficient environment to develop such a complex parallel application.
In this paper, we study the development of a parallel 3-phase black oil reservoir simulator on unstructured meshes. Our work is based on the Trilinos project which provides an object-oriented software framework of integrated algorithms for the solution of large-scale complex multi-physics engineering and scientific problems on massively parallel computing platforms. Trilinos addresses two fundamental issues of developing software for these problems: (i) providing a streamlined process and set of tools for development of new algorithmic implementations and (ii) promoting interoperability of independently developed software packages.
The ability to rapidly incorporate different packages and methods in the Trilinos framework allowed leveraging implementation of computationally intensive modules and development of reservoir simulator in remarkably short timeframe, reducing the development cycle from months to weeks. Our study illustrates how the combination of very efficient state-of-the-art nonlinear solvers with robust partitioning methods, sparse linear solvers, and preconditioning techniques implemented in the Trilinos framework can be used to prototype new computational technologies in a very time efficient manner. Computational tests demonstrate that leveraging parallel computational modules form Trilinos produced computationally efficient and scalable parallel reservoir simulation.
In this paper an algebraic substructuring preconditioner is considered for nonconforming finite element approximations of second-order elliptic problems in 3D domains with diagonal anisotropic diffusion tensor. Using a block Gauss elimination and a substructuring idea, part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent matrix. When the domain considered is a parallelepiped and boundary conditions are uniform on each of the faces, this matrix is separable. Explicit estimates of condition numbers and implementation algorithms are established for the constructed preconditioner. It is shown that the condition number of the preconditioned matrix depends neither on the mesh-size parameter nor on the coefficients of the diffusion tensor. The numerical experiments show that proposed preconditioner is rather efficient and can be used to develop iteration solvers for general second-order elliptic equations on domains, topologically equivalent to a parallelepiped.
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