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Parallelization of Spectral Element Methods
2003Spectral element methods allow for effective implementation of numerical techniques for partial differential equations on parallel architectures. We present two implementations of the parallel algorithm where the communications are performed using MPI. In the first implementation, each processor deals with one element.
Stéphane Airiau +3 more
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A Spectral-Element Method for Transmission Eigenvalue Problems
Journal of Scientific Computing, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jing An, Jie Shen 0001
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Dispersion Analysis for Discontinuous Spectral Element Methods
Journal of Scientific Computing, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
D. Stanescu +2 more
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Spectral Element Methods on Simplicial Meshes
2013We present a review in the construction of accurate and efficient multivariate polynomial approximations on elementary domains that are not Cartesian products of intervals, such as triangles and tetrahedra. After the generalities for high-order nodal interpolation of a function over an interval, we introduce collapsed coordinates and warped tensor ...
Rapetti, Francesca, Pasquetti, Richard
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1997
We analyze the discretization of elliptic boundary-value problems defined in domains with a complicated shape, via a domain decomposition approach. The approximated solution is a patchwork of different algebraic polynomials defined in the subdomains and is determined as the result of a preconditioned iterative procedure.
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We analyze the discretization of elliptic boundary-value problems defined in domains with a complicated shape, via a domain decomposition approach. The approximated solution is a patchwork of different algebraic polynomials defined in the subdomains and is determined as the result of a preconditioned iterative procedure.
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Spectral Finite Element Method
2018In this chapter we describe a method to obtain the solution of second order linear differential equations by means of expansions into sets of Lagrange polynomials called discrete variable representation (DVR). The coefficients of the expansion are obtained by a Galerkin method.
George Rawitscher +2 more
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Application of the hybrid spectral integral method with spectral element method
2007 IEEE Antennas and Propagation Society International Symposium, 2007Exact radiation boundary conditions are of great interest to the numerical solution of Maxwell's equations for an unbounded domain. Previously, the boundary element method has been used as an exact radiation boundary condition in the finite element method.
null Jianguo Liu +4 more
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2009
Chapter 8 introduces multidomain methods to compute problems in geometries that are more complex than a quadrilateral with curved sides. In multidomain spectral methods, and spectral element methods in particular, the domain of interest is subdivided into smaller subdomains that are mapped individually onto the square, allowing problems in truly ...
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Chapter 8 introduces multidomain methods to compute problems in geometries that are more complex than a quadrilateral with curved sides. In multidomain spectral methods, and spectral element methods in particular, the domain of interest is subdivided into smaller subdomains that are mapped individually onto the square, allowing problems in truly ...
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Spectral and Discontinuous Spectral Element Methods for Fractional Delay Equations
SIAM Journal on Scientific Computing, 2014We first develop a spectrally accurate Petrov--Galerkin spectral method for fractional delay differential equations (FDDEs). This scheme is developed based on a new spectral theory for fractional Sturm--Liouville problems (FSLPs), which has been recently presented in [M. Zayernouri and G. E. Karniadakis, J. Comput. Phys., 252 (2013), pp.
Mohsen Zayernouri +3 more
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2010
The spectral-element method is a high-order numerical method that allows us to solve the seismic wave equation in 3D heterogeneous Earth models. The method enables adaptation of the mesh to the irregular surface topography and to the variable wavelengths inside the Earth. Moreover, the spectral-element method yields accurate solutions for surface waves
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The spectral-element method is a high-order numerical method that allows us to solve the seismic wave equation in 3D heterogeneous Earth models. The method enables adaptation of the mesh to the irregular surface topography and to the variable wavelengths inside the Earth. Moreover, the spectral-element method yields accurate solutions for surface waves
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