
Stability of explicit RungeKutta methods for high order finite element approximation of linear parabolic equations
We study the stability of explicit RungeKutta methods for high order La...
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Spectral analysis of continuous FEM for hyperbolic PDEs: influence of approximation, stabilization, and timestepping
We study continuous finite element dicretizations for one dimensional hy...
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Moment fitted cut spectral elements for explicit analysis of guided wave propagation
In this work, a method for the simulation of guided wave propagation in ...
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Structured inversion of the Bernstein mass matrix
Bernstein polynomials, long a staple of approximation theory and computa...
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Fast BarycentricBased Evaluation Over Spectral/hp Elements
As the use of spectral/hp element methods, and highorder finite element...
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Highorder implicit time integration scheme based on Padé expansions
A singlestep highorder implicit time integration scheme for the soluti...
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Easy and Efficient preconditioning of the Isogeometric Mass Matrix
This paper deals with the fast solution of linear systems associated wit...
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A HighOrder LowerTriangular PseudoMass Matrix for Explicit Time Advancement of hp Triangular Finite Element Methods
Explicit time advancement for continuous finite elements requires the inversion of a global mass matrix. For spectral element simulations on quadrilaterals and hexahedra, there is an accurate approximate mass matrix which is diagonal, making it computationally efficient for explicit simulations. In this article it is shown that for the standard space of polynomials used with triangular elements, denoted T(p) where p is the degree of the space, there is no diagonal approximate mass matrix that permits accurate solutions. Accuracy is defined as giving an exact projection of functions in T(p1). In light of this, a lowertriangular pseudomass matrix method is introduced and demonstrated for the space T(3). The pseudomass matrix and accompanying highorder basis allow for computationally efficient timestepping techniques without sacrificing the accuracy of the spatial approximation for unstructured triangular meshes.
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