... matrix AMG ILU equation factorization Introduction Solution approaches based on algebraic multigrid (AMG) have demonstrated to be efficient methods for solving linear systems in reservoir simulations. Especially the continuous growth in size and complexity of such simulations creates a need...

... r = diagonal row equilibration matrix L = lower triangular matrix M = preconditioner p = maximum of entries in row or column in LU factorization P = permutation matrix U = upper triangular matrix W T = restriction matrix x = solution vector τ...

...-like equation is formed from the fully implicit matrix algebraically. For a commercial reservoir simulator, this first stage pressure equation is solved by the Algebraic Multi-Grid (AMG) method 4 , 5 . The second stage preconditioner uses Incomplete LU(K) factorization 3 for the fully implicit...

... flow in porous media polynomial iteration Fluid Dynamics simulator heterogeneous architecture Implementation GPU version Upstream Oil & Gas Library parallelism solver matrix factorization architecture reservoir simulation reservoir simulator cpu version algorithm...

... is the vertical depth, and q p is the phase source per unit volume. After standard finite-volume discretization on a mesh, we obtain Abstract We describe a massively parallel Nested Factorization (NF) linear solver for large systems of equations. NF is a powerful classic preconditioner receiving...

... implements the most efficient Additive Schwarz algorithms. RecursiveFILU is based on non-overlapping domain decomposition paradigm with parallel truncated factorization of the domain matrices and factorization of the interface matrix. MultiLevelILUC and MultiLevelRIC implement a parallel multilevel framework...

... reservoir simulator mpnf algorithm reservoir simulation gpu parallelism appleyard tridiagonal iteration matrix assembly matrix upstream oil & gas kernel hydrocarbon component grid block implementation solver factorization preconditioner Introduction The size...

... complex eor process spe 93023 linear solver factorization refinement grid cell sammon solver splitting parallel solver amalgamation reservoir simulation grabenstetter Introduction Dynamic gridding techniques have been shown to speed up both isothermal 1 and thermal 2...

... non-parallel black-oil simulator to achieve parallel execution are discussed, as are the techniques for achieving good parallel speedups for simulator tasks such as building the Jacobian matrix. The simulator uses a parallel implementation of a variable degree incomplete LU (ILU) factorization...

... overhead to the full simulation run without gradients. Direct Gauss elimination solvers can be used to address this problem by performing the factorization of the matrix only once and then reusing the factored matrix for the solution of the multiple right hand sides. This is a limited technique, however...

... reservoir simulation problems are preconditioned conjugate gradient like methods. However, the more robust preconditioners such as nested factorization and ILU factorization are not suitable for parallel computers. This paper describes a parallel linear equation solver that is suitable for large and small...

... This formula describes the outer (or third) level of factorization. The middle level can be defined in the similar manner B γ = ( − L γ β , B γ β ] [ B γ β ] − 1 [ B γ β , − U γ β ) Finally each inner level forms the product...

... The matrix blocks correspond to diagonal groups of z-lines and thus the T i consist of n i independent nz × nz tridiagonals. We approximately factor A ≈ LU as follows: (2) A = M 1 Q 2 M 2 · · · · Q N M N...

... Abstract The objective of this work was to develop improved variations of the BEPS, FAC, and Sequential preconditioning methods used to solve composite grid linear systems. These methods are attractive since they use standard subgrid approximate factorizations in constructing the composite grid...

... of performance and complexity is made with the best solvers now in widespread use in reservoir simulation. symposium scientific computing nested factorization rs ilu equation matrix grid coefficient multigrid application interpolation relaxation multigrid method algorithm upstream oil...

... Abstract This paper presents an incomplete LU factorization (ILU) technique coupled with generalized conjugate gradient acceleration especially designed for linear equations resulting from locally refined grids. The factorization is based on a special ordering scheme. This repeated red black...

... refinement refinement local refinement upstream oil & gas subblock level subblock spe symposium reservoir simulation breakthrough time grid refinement flexible approach factorization subdivision saturation matrix dynamic local refinement local grid refinement INTRODUCTION...

..., are presented to validate the method. Several comparisons are made with other well-known preconditioners including incomplete LU and reduced system/incomplete LU factorizations. For the examples considered the domain decomposition technique was the most efficient in a nonparallel environment; in a parallel...

... Abstract Two recently developed methods for the solution of the sparse block-banded linear equation sets generated by fully implicit reservoir simulators are investigated. Nested factorization is a new approach to forming an incomplete factorization of the linear system. Comparisons are made...

... and neq is the number of coupled equations at each node. x 2 and b 2 are of length nw, the number of well unknowns. The total number of unknowns is: (3) N = n * neq + nw The system of equations (2) is factored as: (4) [ A W 2 W 1 W...