A method of finite element tearing and interconnecting and its parallel solution algorithm

Farhat, Charbel; Roux, François‐Xavier

doi:10.1002/nme.1620320604

Cited by 1,095 publications

(838 citation statements)

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“…The Boundary Element Tearing and Interconnecting Method (BETI) is a domain decomposition method based on the Symmetric Galerkin BEM [4] similar to the Finite Element Tearing and Interconnecting Method (FETI) for the FEM introduced by [5]. In this work the collocation BEM is used to set up the equation system similar to the original BETI method.…”

Section: Boundary Element Tearing and Interconnecting Methods (Beti)mentioning

confidence: 99%

Modelling the Process of Sequential Excavation With the Boundary Element Method

Duenser

Beer

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The Boundary Element Method (BEM) is ideally suited for the simulation of underground constructions like tunnels or caverns. Such structures are modelled with the BEM inside an infinite or semi-infinite domain. As the radiation condition is fulfilled by the BEM no truncation of the domain is necessary. Only the surface of the structure (e.g. tunnel) has to be discretised by boundary elements (BE). An accurate simulation of the tunnelling process has to consider the sequential excavation where parts of the rock mass are excavated at different time and location. This special constructional condition has a direct influence onto the simulation model. In this work different methods are presented which consider the sequential excavation. The first method is the discretisation of the problem by multiple BE regions (MRBEM). Each region, which will be excavated during the excavation process, is discretised by a separate finite BE region. These regions are embedded inside an infinite region which represent the infinite extend of the domain. Thus, a system of BE regions arise which have to be coupled at their common interfaces. Two coupling strategies, the Boundary Element Tearing and Interconnecting Method (BETI) and the method of Interface Coupling (IC) will be presented to solve the sequential tunnel excavation. The second method uses only a single BE region (SRBEM) for every step of excavation. For each load step the geometry/mesh has to be updated. Thus, the mesh of the previous load step will be extended by the surface of the new excavation volume of the current load step. Beside the geometry update an essential part of this method is an accurate evaluation of the excavation loading. The excavation loads for each excavation step are tractions applied at the part of the boundary surface just generated by the geometry update. These tractions depend on all previous load steps and will be evaluated by a calculation of internal results in the interior of the single region. The internal results can be either stresses or displacements. In this work the modelling strategies of the MRBEM and SRBEM approach will be presented. On a realistic tunnel example the accuracy of the results for the mentioned methods will be shown as well as the performance of the calculations. 3168

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Section: Boundary Element Tearing and Interconnecting Methods (Beti)mentioning

confidence: 99%

Modelling the Process of Sequential Excavation With the Boundary Element Method

Duenser

Beer

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…FETI-1 [13,14,12,23] is a non-overlapping DDM [16]. Thus, it is based on decomposing the original spatial domain into non-overlapping subdomains.…”

Section: Permonfllopmentioning

confidence: 99%

“…PERMON extends PETSc [3] with support for quadratic programming (QP) and non-overlapping domain decomposition methods (DDM), namely of the FETI (Finite Element Tearing and Interconnecting) [13,12,5,24] type. This paper presents the process of solving contact problems using PERMON (Section 3).…”

Section: Introductionmentioning

confidence: 99%

Solving Contact Mechanics Problems with PERMON

Hapla

Horák

Pospíšil

et al. 2016

Lecture Notes in Computer Science

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Abstract. PERMON makes use of theoretical results in quadratic programming algorithms and domain decomposition methods. It is built on top of the PETSc framework for numerical computations. This paper describes its fundamental packages and shows their applications. We focus here on contact problems of mechanics decomposed by means of a FETI-type nonoverlapping domain decomposition method. These problems lead to inequality constrained quadratic programming problems that can be solved by our PermonQP package.

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“…This transforms (4) into a saddle point problem; see [5,7,8]. Such a choice is perfectly admissible for matching interfaces but is prone to difficulties when Γ c 1 = Γ c 2 because the approximation of H −1/2 (Γ c ) cannot be "split" between the two distinct interfaces.…”

Section: A Matching Interface Problem For the Poisson Equationmentioning

confidence: 99%

“…The strong problem (2)- (3) does not admit a natural extension to this case and so, to obtain a formal statement of the interface problem we proceed with the weak saddle-point equation (5).…”

Section: A Non-matching Interface Problem Of the Poisson Equationmentioning

confidence: 99%