Spectral‐domain decomposition methods for the solution of acoustic and elastic wave equations

Geophysics ◽  
1996 ◽  
Vol 61 (4) ◽  
pp. 1160-1174 ◽  
Author(s):  
Ezio Faccioli ◽  
Fabio Maggio ◽  
Alfio Quarteroni ◽  
Aldo Taghan
Keyword(s):  
Domain Decomposition ◽  
Wave Equations ◽  
Heterogeneous Media ◽  
Domain Decomposition Method ◽  
Decomposition Methods ◽  
Spectral Domain ◽  
Test Cases ◽  
Domain Decomposition Methods ◽  
Elastic Wave Equations ◽  
The Stability

A new spectral‐domain decomposition method is presented for acoustic and elastodynamic wave propagation in 2-D heterogeneous media. Starting from a variational formulation of the problem, two different approaches are proposed for the spatial discretization: a mixed Fourier‐Legendre and a full Legendre collocation. The matching conditions at subdomain interfaces are carefully analyzed, and the stability and efficiency of time‐advancing schemes are investigated. The numerical validation with some significant test cases illustrates the accuracy, flexibility, and robustness of our methods. These allow the treatment of complex geometries and heterogeneous media while retaining spectral accuracy.

scholarly journals Barycentric spectral domain decomposition methods for valuing a class of infinite activity Lévy models

2019 ◽  
Vol 12 (3) ◽  
pp. 625-643 ◽  
Author(s):  
Edson Pindza ◽  
◽  
Francis Youbi ◽  
Eben Maré ◽  
Matt Davison ◽  
...  
Keyword(s):  
Domain Decomposition ◽  
Decomposition Methods ◽  
Spectral Domain ◽  
Domain Decomposition Methods

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.

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

scholarly journals Exponentially convergent non overlapping domain decomposition methods for the Helmholtz equation

2020 ◽  
Vol 54 (3) ◽  
pp. 775-810 ◽  
Author(s):  
Francis Collino ◽  
Patrick Joly ◽  
Matthieu Lecouvez
Keyword(s):  
Domain Decomposition ◽  
General Framework ◽  
Domain Decomposition Method ◽  
Integral Operators ◽  
Decomposition Methods ◽  
Domain Decomposition Methods ◽  
Convergent Method ◽  
Non Local ◽  
Overlapping Domain Decomposition ◽  
Well Posed

In this paper, we develop in a general framework a non overlapping Domain Decomposition Method that is proven to be well-posed and converges exponentially fast, provided that specific transmission operators are used. These operators are necessarily non local and we provide a class of such operators in the form of integral operators. To reduce the numerical cost of these integral operators, we show that a truncation process can be applied that preserves all the properties leading to an exponentially fast convergent method. A modal analysis is performed on a separable geometry to illustrate the theoretical properties of the method and we exhibit an optimization process to further reduce the convergence rate of the algorithm.

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