In this article, we use the direct coupling of local discontinuous Galerkin (LDG) and natural boundary element method (NBEM) to solve a class of three-dimensional interfaceproblem, which involves a nonlinearproblem ...
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In this article, we use the direct coupling of local discontinuous Galerkin (LDG) and natural boundary element method (NBEM) to solve a class of three-dimensional interfaceproblem, which involves a nonlinearproblem in a bounded domain and a Poisson equation in an unbounded domain. A spherical surface as an artificial boundary is introduced. The coupled discrete primal formulation on a bounded domain is obtained. The well-posedness of the primal formulation is verified. The optimal error order with respect to energy norm is given. Numerical examples are presented to demonstrate the optimal convergent rates. (C) 2015 Elsevier Inc. All rights reserved.
In this paper, we introduce a domain decomposition method with non-matching grids for a certain nonlinear interface problem in unbounded domains. To solve this problem, we discuss a new coupling of finite element meth...
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In this paper, we introduce a domain decomposition method with non-matching grids for a certain nonlinear interface problem in unbounded domains. To solve this problem, we discuss a new coupling of finite element method(FE) and natural boundary element(NBE). We first derive the optimal energy error estimate of finite element approximation to the coupled FEM-NBEM problem. Then we use a dual basis multipier on the interface to provide the numerical analysis with non-matching grids. Finally, we give some numerical examples further to confirm our theoretical results.
In this paper, we apply the artificial boundary method to solve a three-dimensional nonlinear interface problem on an unbounded domain. A spherical or ellipsoidal surface as the artificial boundary is introduced. The ...
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In this paper, we apply the artificial boundary method to solve a three-dimensional nonlinear interface problem on an unbounded domain. A spherical or ellipsoidal surface as the artificial boundary is introduced. The exact artificial boundary conditions are derived explicitly in terms of an infinite series and then the well-posedness of the coupled weak formulation in a bounded domain, which is equivalent to the original problem in the unbounded domain, is obtained. The error estimate depends on the mesh size, the term after truncating the infinite series and the location of the artificial boundary. Some numerical examples are presented to demonstrate the effectiveness and accuracy of this method.
We present an efficient approach for preconditioning systems arising in multiphase flow in a parallel domain decomposition framework known as the mortar mixed finite element method. Subdomains are coupled together wit...
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We present an efficient approach for preconditioning systems arising in multiphase flow in a parallel domain decomposition framework known as the mortar mixed finite element method. Subdomains are coupled together with appropriate interface conditions using mortar finite elements. These conditions are enforced using an inexact Newton-Krylov method, which traditionally required the solution of nonlinear subdomain problems on each interface iteration. A new preconditioner is formed by constructing a multiscale basis on each subdomain for a fixed Jacobian and time step. This basis contains the solutions of nonlinear subdomain problems for each degree of freedom in the mortar space and is applied using an efficient linear combination. Numerical experiments demonstrate the relative computational savings of recomputing the multiscale preconditioner sparingly throughout the simulation versus the traditional approach.
In this work, we consider compressible single-phase flow problems in a porous medium containing a fracture. In the fracture, a nonlinear pressure-velocity relation is prescribed. Using a non-overlapping domain decompo...
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In this work, we consider compressible single-phase flow problems in a porous medium containing a fracture. In the fracture, a nonlinear pressure-velocity relation is prescribed. Using a non-overlapping domain decomposition procedure, we reformulate the global problem into a nonlinear interface problem. We then introduce two new algorithms that are able to efficiently handle the nonlinearity and the coupling between the fracture and the matrix, both based on linearization by the so-called L-scheme. The first algorithm, named MoLDD, uses the L-scheme to resolve for the nonlinearity, requiring at each iteration to solve the dimensional coupling via a domain decomposition approach. The second algorithm, called ItLDD, uses a sequential approach in which the dimensional coupling is part of the linearization iterations. For both algorithms, the computations are reduced only to the fracture by precomputing, in an offline phase, a multiscale flux basis (the linear Robin-to-Neumann codimensional map), that represent the flux exchange between the fracture and the matrix. We present extensive theoretical findings X and in particular, t. The stability and the convergence of both schemes are obtained, where user-given parameters are optimized to minimize the number of iterations. Examples on two important fracture models are computed with the library PorePy and agree with the developed theory.
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