scholarly journals About Revisiting Domain Decomposition Methods for Poroelasticity

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 187
Author(s):  
Horacio Florez
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Computational Cost ◽  
Decomposition Methods ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Coupled Flow ◽  
Advantages And Disadvantages ◽  
Reservoir Compaction ◽  
Mortar Finite Element Method

In this paper, we revisit well-established domain decomposition (DD) schemes to perform realistic simulations of coupled flow and poroelasticity problems on parallel computers. We define distinct solution schemes to take into account different transmission conditions among subdomain boundaries. Indeed, we examine two different approaches, i.e., Dirichlet-Neumann (DN) and the mortar finite element method (MFEM), and we recognize their advantages and disadvantages. The MFEM significantly lessens the computational cost of reservoir compaction and subsidence calculations by dodging the conforming Cartesian grids that arise from the pay-zone onto its vicinity. There is a manifest necessity of producing non-matching interfaces between the reservoir and its neighborhood. We thus employ MFEM over nonuniform rational B-splines (NURBS) surfaces to stick these non-conforming subdomain parts. We then decouple the mortar saddle-point problem (SPP) using the Dirichlet-Neumann domain decomposition (DNDD) scheme. We confirm that this procedure is proper for calculations at the field level. We also carry comprehensive comparisons between the conventional and non-matching solutions to prove the method’s accuracy. Examples encompass linking finite element codes for slightly compressible single-phase and poroelasticity. We have used this program to a category of problems ranking from near-borehole applications to whole field subsidence estimations.

scholarly journals Domain decomposition and multiscale mortar mixed finite element methods for linear elasticity with weak stress symmetry

2019 ◽  
Vol 53 (6) ◽  
pp. 2081-2108
Author(s):  
Eldar Khattatov ◽  
Ivan Yotov
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Normal Stress ◽  
Linear Elasticity ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Decomposition Methods ◽  
Interface Problem ◽  
Element Formulation ◽  
Element Space

Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier to impose interface continuity of normal stress or displacement, respectively. By eliminating the interior subdomain variables, the global problem is reduced to an interface problem, which is then solved by an iterative procedure. The condition number of the resulting algebraic interface problem is analyzed for both methods. A multiscale mortar mixed finite element method for the problem of interest on non-matching multiblock grids is also studied. It uses a coarse scale mortar finite element space on the non-matching interfaces to approximate the trace of the displacement and impose weakly the continuity of normal stress. A priori error analysis is performed. It is shown that, with appropriate choice of the mortar space, optimal convergence on the fine scale is obtained for the stress, displacement, and rotation, as well as some superconvergence for the displacement. Computational results are presented in confirmation of the theory of all proposed methods.

A Constrained Finite Element Method Based on Domain Decomposition Satisfying the Discrete Maximum Principle for Diffusion Problems

2015 ◽  
Vol 18 (2) ◽  
pp. 297-320
Author(s):  
Xingding Chen ◽  
Guangwei Yuan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Maximum Principle ◽  
Domain Decomposition ◽  
Decomposition Methods ◽  
Discontinuous Coefficients ◽  
Discrete Maximum Principle ◽  
Diffusion Tensors ◽  
Diffusion Problems ◽  
Element Method

AbstractIn this paper, we are concerned with the constrained finite element method based on domain decomposition satisfying the discrete maximum principle for diffusion problems with discontinuous coefficients on distorted meshes. The basic idea of domain decomposition methods is used to deal with the discontinuous coefficients. To get the information on the interface, we generalize the traditional Neumann-Neumann method to the discontinuous diffusion tensors case. Then, the constrained finite element method is used in each subdomain. Comparing with the method of using the constrained finite element method on the global domain, the numerical experiments show that not only the convergence order is improved, but also the nonlinear iteration time is reduced remarkably in our method.

scholarly journals Non-conformal domain decomposition methods for time-harmonic Maxwell equations

2012 ◽  
Vol 468 (2145) ◽  
pp. 2433-2460 ◽  
Author(s):  
Yang Shao ◽  
Zhen Peng ◽  
Kheng Hwee Lim ◽  
Jin-Fa Lee
Keyword(s):  
Integral Equation ◽  
Finite Element ◽  
Domain Decomposition ◽  
Wave Scattering ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Decomposition Methods ◽  
Domain Decomposition Methods ◽  
Surface Integral ◽  
Scattering Problems

We review non-conformal domain decomposition methods (DDMs) and their applications in solving electrically large and multi-scale electromagnetic (EM) radiation and scattering problems. In particular, a finite-element DDM, together with a finite-element tearing and interconnecting (FETI)-like algorithm, incorporating Robin transmission conditions and an edge corner penalty term , are discussed in detail. We address in full the formulations, and subsequently, their applications to problems with significant amounts of repetitions. The non-conformal DDM approach has also been extended into surface integral equation methods. We elucidate a non-conformal integral equation domain decomposition method and a generalized combined field integral equation method for modelling EM wave scattering from non-penetrable and penetrable targets, respectively. Moreover, a plane wave scattering from a composite mockup fighter jet has been simulated using the newly developed multi-solver domain decomposition method.

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

scholarly journals Finite Element Tearing and Interconnecting Method and its Algorithms for Parallel Solution of Magnetic Field Problems

2013 ◽  
Vol 3 (1) ◽  
pp. 25-30
Author(s):  
Dániel Marcsa ◽  
Miklós Kuczmann
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Domain Decomposition ◽  
Data Exchange ◽  
Domain Decomposition Method ◽  
Decomposition Methods ◽  
Engineering Practice ◽  
Domain Decomposition Methods ◽  
Parallel Solution ◽  
Solution Algorithms

Abstract Because of the exponential increase of computational resource requirement for numerical field simulations of more and more complex physical phenomena and more and more complex large problems in science and engineering practice, parallel processing appears to be an essential tool to handle the resulting large-scale numerical problems. One way of parallelization of sequential (singleprocessor) finite element simulations is the use of domain decomposition methods. Domain decomposition methods (DDMs) for parallel solution of linear systems of equations are based on the partitioning of the analyzed domain into sub-domains which are calculated in parallel while doing appropriate data exchange between those sub-domains. In this case, the non-overlapping domain decomposition method is the Lagrange multiplier based Finite Element Tearing and Interconnecting (FETI) method. This paper describes one direct solver and two parallel solution algorithms of FETI method. Finally, comparative numerical tests demonstrate the differences in the parallel running performance of the solvers of FETI method. We use a single-phase transformer and a three-phase induction motor as twodimensional static magnetic field test problems to compare the solvers

Simulation and computational heat transfer in the human eye with Dirichlet–Neumann domain decomposition approximation

2019 ◽  
Vol 10 (06) ◽  
pp. 1950041
Author(s):  
Salem Ahmedou Bamba ◽  
Abdellatif Ellabib
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Domain Decomposition Method ◽  
Mathematical Formulation ◽  
Finite Element Approximation ◽  
Decomposition Methods ◽  
Element Approximation ◽  
Numerical Application ◽  
Human Eye ◽  
Uniqueness Of The Solution

In this paper, a bioheat model of temperature distribution in the human eye is studied, the mathematical formulation of this model is described using adequate mathematical tools. The existence and the uniqueness of the solution of this problem is proven and four algorithms based on finite element method approximation and domain decomposition methods are presented in details. The validation of all algorithm is done using a numerical application for an example where the analytical solution is known. The properties and parameters reported in the open literature for the human eye are used to approximate numerically the temperature for bioheat model by finite element approximation and nonoverlapping domain decomposition method. The obtained results that are verified using the experimental results recorded in the literature revealed a better accuracy by the use of algorithm proposed.

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