Domain Decomposition and Schur Complement Approaches to Coupling the Well Equations in Reservoir Simulation

1995 ◽  
Vol 16 (1) ◽  
pp. 29-39 ◽  
Author(s):  
J. C. Díaz ◽  
K. Shenoi
Keyword(s):  
Domain Decomposition ◽  
Reservoir Simulation ◽  
Schur Complement

Fast Domain Decomposition Type Solver for Stiffness Matrices of Reference p-Elements

2013 ◽  
Vol 13 (2) ◽  
pp. 161-183 ◽  
Author(s):  
Vadim Korneev
Keyword(s):  
Finite Difference ◽  
Domain Decomposition ◽  
Elliptic Equations ◽  
Harmonic Functions ◽  
Schur Complement ◽  
P Elements ◽  
Stiffness Matrices ◽  
The Family ◽  
Discrete Harmonic Functions

Abstract. A key component of domain decomposition solvers for hp discretizations of elliptic equations is the solver for internal stiffness matrices of p-elements. We consider an algorithm which belongs to the family of secondary domain decomposition solvers, based on the finite-difference like preconditioning of p-elements, and was outlined by the author earlier. We remove the uncertainty in the choice of the coarse (decomposition) grid solver and suggest the new interface Schur complement preconditioner. The latter essentially uses the boundary norm for discrete harmonic functions induced by orthotropic discretizations on slim rectangles, which was derived recently. We prove that the algorithm has linear arithmetical complexity.

scholarly journals Direct Schur complement method by domain decomposition based on H-matrix approximation

2005 ◽  
Vol 8 (3-4) ◽  
pp. 179-188 ◽  
Author(s):  
Wolfgang Hackbusch ◽  
Boris N. Khoromskij ◽  
Ronald Kriemann
Keyword(s):  
Domain Decomposition ◽  
Schur Complement ◽  
Matrix Approximation

A Domain Decomposition of the Finite Element-Boundary Integral Method for Scattering by Deep Cavities

2011 ◽  
Vol 383-390 ◽  
pp. 2585-2589
Author(s):  
Zhi Wei Cui ◽  
Yi Ping Han ◽  
Wen Juan Zhao
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Domain Decomposition Method ◽  
Schur Complement ◽  
Building Blocks ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Special Method ◽  
Deep Cavities ◽  
Element Boundary

An efficient domain decomposition method (DDM) is employed to improve upon the efficiency and capability of the finite element-boundary integral (FE-BI) method for calculation of electromagnetic (EM) scattering from deep cavities. This method first subdivides the original cavity into many sub-domains along its depth and classifies these sub-domains into a few building blocks. It then employs the substructuring method to deal with the different types of sub-domains. The resulting Schur complement system is solved by a special method which has low memory requirements because the formation of the global Schur complement matrix is not necessary. Numerical results indicate that the presented method is an effective approach for scattering by deep cavities.

An Adaptive Sequential Fully Implicit Domain-Decomposition Solver

SPE Journal ◽  
2021 ◽  
pp. 1-13
Author(s):  
Ø. S. Klemetsdal ◽  
A. Moncorgé ◽  
H. M. Nilsen ◽  
O. Møyner ◽  
K-. A. Lie
Keyword(s):  
Domain Decomposition ◽  
Reservoir Simulation ◽  
Rock Properties ◽  
Solution Strategy ◽  
Flow And Transport ◽  
Solution Strategies ◽  
Fully Implicit ◽  
Fluid Behavior ◽  
Nonlinear Solver ◽  
Nonlinear Solvers

Summary Modern reservoir simulation must handle complex compositional fluid behavior, orders-of-magnitude variations in rock properties, and large velocity contrasts. We investigate how one can use nonlinear domain-decomposition preconditioning to combine sequential and fully implicit (FI) solution strategies to devise robust and highly efficient nonlinear solvers. A full simulation model can be split into smaller subdomains that each can be solved independently, treating variables in all other subdomains as fixed. In subdomains with weaker coupling between flow and transport, we use a sequential fully implicit (SFI) solution strategy, whereas regions with stronger coupling are solved with an FI method. Convergence to the FI solution is ensured by a global update that efficiently resolves long-range interactions across subdomains. The result is a solution strategy that combines the efficiency of SFI and its ability to use specialized solvers for flow and transport with the robustness and correctness of FI. We demonstrate the efficacy of the proposed method through a range of test cases, including both contrived setups to test nonlinear solver performance and realistic field models with complex geology and fluid physics. For each case, we compare the results with those obtained using standard FI and SFI solvers. This paper is published as part of the 2021 Reservoir Simulation Conference Special Issue.

Domain Decomposition Methods Applied To Coupled Flow-Geomechanics Reservoir Simulation

2011 ◽  
Author(s):  
Horacio Florez ◽  
Mary Fanett Wheeler ◽  
Adolfo Antonio Rodriguez ◽  
Jorge Eduardo Palomino Monteagudo
Keyword(s):  
Domain Decomposition ◽  
Reservoir Simulation ◽  
Decomposition Methods ◽  
Domain Decomposition Methods ◽  
Coupled Flow
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