An Iterative Procedure with Interface Relaxation for Domain Decomposition Methods

“…This means that S (2) must be, in some sense, larger than S (1) . Suppose the two domains are geometrically symmetric, with the same thermal conductivity, then the S (1) and S (2) matrices are identical. If the thermal conductivity is different from one domain to the other, the ratio between the two matrices is equal to the ratio between the thermal conductivity of both domains.…”

Section: Given Xmentioning

confidence: 99%

“…It can be the case, even though S (2) is not larger than S (1) , provided that the augmentation matrix A (2) 33 is close to the Shur complement of domain Ω 1 , S (1) .…”

Section: Robin Boundary Conditionmentioning

confidence: 99%

“…If A (2) 33 = S (1) , the method converges in only one iteration: it is a direct method. This property can be also derived from the elimination of inner unknowns of domain Ω 1 in global system (16), that reduces the system as follows in Ω 2 :…”

Section: Robin Boundary Conditionmentioning

confidence: 99%

“…In the context of domain decomposition method, this methodology is called, for second order PDEs like steady heat equation or linear elasticity, DirichletNeumann iteration [1]. In the second section of this paper standard convergence results for this method will be recalled.…”

Section: Introductionmentioning

confidence: 99%

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Domain Decomposition Methodology with Robin Interface Matching Conditions for Solving Strongly Coupled Problems

Roux

2008

Computational Science – ICCS 2008

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Abstract. In the case of strongly coupled problems like fluid-structure models in aero-elasticity or aero-thermo-mechanics, a standard solution methodology is based on so called Dirichlet-Neumann iterations. This means that, for instance, the velocity at the interface between the two media is imposed in the fluid, the solution of the fluid problem gives a pressure that is imposed at the boundary of the structure, and then the solution of the problem in the structure gives a new velocity to be imposed to the fluid. This method is not always stable, depending on the relative properties of the media, unless a suitable relaxation parameter is introduced. In order to enforce both velocity and pressure continuity at the interface, the matching conditions can be formulated, like in domain decomposition methods, in a mixed form. This means that the boundary conditions derived in one physical domain from the other one is of Robin type. With Robin boundary condition, an interface stiffness, in the case of velocity-pressure conditions, is introduced. The optimal choice for this stiffness can be proved to be, in the case of linear problems, the so called "Dirichlet-Neumann" operator of the opposite domain, this means for the discrete equations, the static condensation on the interface of the domain stiffness matrix. Of course, the static condensation cannot be performed in practice, since it is extremely expensive and that the resulting matrix is dense. But it can be approximated in several ways. The underlying general idea behind that methodology is the following: with Robin boundary conditions on the interface, a constitutive law is imposed on the boundary of each media that should optimally exactly represent the interaction with the other media.

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Mismatching refinement with domain decomposition for the analysis of steady-state metal forming process

Park

Yang

2000

Int. J. Numer. Meth. Engng.

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The "nite element analysis of three-dimensional metal forming processes is generally subject to large computational burden due to its non-linearity. For economic computation, the mismatching re"nement, an e$cient domain decomposition method with di!erent mesh density for each subdomain, is developed in the present study. A modi"ed velocity alternating scheme for the interface treatment is proposed in order to obtain good convergence and accuracy in the mismatching re"nement. As a numerical example, the analysis of the axisymmetric extrusion processes is carried out. The results are discussed for the various velocity update schemes and for the variation of the length of overlapped region. The three-dimensional extrusion processes for a rectangular section and an E-section are analysed in order to verify the e!ectiveness of the proposed method. Comparing the results with those of the conventional method of full region analysis, the accuracy and the computational e$ciency of the proposed method are then discussed.

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An Iterative Procedure with Interface Relaxation for Domain Decomposition Methods

Cited by 143 publications

References 8 publications

Domain Decomposition Methods for Domain Composition Purpose: Chimera, Overset, Gluing and Sliding Mesh Methods

Domain Decomposition Methods for Domain Composition Purpose: Chimera, Overset, Gluing and Sliding Mesh Methods

Domain Decomposition Methodology with Robin Interface Matching Conditions for Solving Strongly Coupled Problems

Mismatching refinement with domain decomposition for the analysis of steady-state metal forming process

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