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ARBITRARY HIGHORDER FINITE ELEMENT SCHEMES AND HIGHORDER MASS LUMPING SÉBASTIEN JUND,
"... Computers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with highorder methods. In this article we will consider Lagrange finite elements of order k and show how it is possible to automatically generate the mass and stiffness matrices of any or ..."
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Computers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with highorder methods. In this article we will consider Lagrange finite elements of order k and show how it is possible to automatically generate the mass and stiffness matrices of any
DISPERSIVE BEHAVIOUR OF HIGH ORDER FINITE ELEMENT SCHEMES FOR THE ONEWAY WAVE EQUATION
"... Abstract. We study the ability of high order numerical methods to propagate discrete waves at the same speed as the physical waves in the case of the oneway wave equation. A detailed analysis of the finite element method is presented including an explicit form for the discrete dispersion relation a ..."
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Abstract. We study the ability of high order numerical methods to propagate discrete waves at the same speed as the physical waves in the case of the oneway wave equation. A detailed analysis of the finite element method is presented including an explicit form for the discrete dispersion relation
Highorder
"... spacetime finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling ..."
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spacetime finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling
High Order Finite Element Solution of Elastohydrodynamic Lubrication Problems
, 2006
"... The candidate confirms that the work submitted is his own and that the appropriate credit has been given where reference has been made to the work of others. This copy has been supplied on the understanding that it is copyright material and that In this thesis, a highorder finite element scheme, ba ..."
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The candidate confirms that the work submitted is his own and that the appropriate credit has been given where reference has been made to the work of others. This copy has been supplied on the understanding that it is copyright material and that In this thesis, a highorder finite element scheme
Efficient Implementation of Weighted ENO Schemes
, 1995
"... In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially nonoscillatory) finite difference schemes of Liu, Osher and Chan [9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L¹ norm) ENO schemes are (r +1) th order accur ..."
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Cited by 412 (38 self)
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In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially nonoscillatory) finite difference schemes of Liu, Osher and Chan [9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L¹ norm) ENO schemes are (r +1) th order
Highorder
"... finiteelement seismic wave propagation modeling with MPI on a large GPU cluster ..."
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finiteelement seismic wave propagation modeling with MPI on a large GPU cluster
SOME IMPORTANT PROPERTIES OF HIGHORDER FINITEDIFFERENCE SCHEMES
"... An inherent contradiction in the finitedifference methods for the Laplace equation is demonstrated. The grid size in a practical computation must, on the one hand, be fine enough to ensure the numerical accuracy, but, on the other hand, be necessarily large to avoid an illconditioned difference eq ..."
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equation system, Higherorder schemes are shown to be advantageous in terms of both the accuracy and the condition of the difference equation system. where aH, av and (J are coefficients depending on the shape of the grid element. Typical Schemes
Parallel Shape Optimization of ThreeDimensional Continua with HighOrder Finite Elements
"... This contribution is on shape optimization of 3D continua using highorder finite elements. Since in the pversion of FEM the discretization error is controlled by raising the polynomial degree, adaptive remeshing procedures during optimization are not required. The element geometry is constructed u ..."
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independent from the finite element mesh. A two level parallel scheme is employed in order to run the optimization on a cluster computer with about 100 CPUs. 2. Keywords: Highorder FEM, 3D shape optimization, NURBS, parallel computing. Shape optimization of continuous structures requires careful attention
GPUBased Volume Visualization from HighOrder Finite Element Fields
"... Abstract—This paper describes a new volume rendering system for spectral/hp finiteelement methods that has as its goal to be both accurate and interactive. Even though highorder finite element methods are commonly used by scientists and engineers, there are few visualization methods designed to di ..."
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Abstract—This paper describes a new volume rendering system for spectral/hp finiteelement methods that has as its goal to be both accurate and interactive. Even though highorder finite element methods are commonly used by scientists and engineers, there are few visualization methods designed
Renormalization in quantum field theory and the RiemannHilbert problem. II. The βfunction, diffeomorphisms and the renormalization group
 Comm. Math. Phys
"... We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann–Hilbert problem. Given a loop γ(z), z  = 1 of elements of a complex Lie group G the general procedure is given by evalu ..."
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Cited by 332 (39 self)
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We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann–Hilbert problem. Given a loop γ(z), z  = 1 of elements of a complex Lie group G the general procedure is given
Results 1  10
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