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Higher-order finite elements for embedded simulation
ACM Transactions on Graphics, 2020As demands for high-fidelity physics-based animations increase, the need for accurate methods for simulating deformable solids grows. While higherorder finite elements are commonplace in engineering due to their superior approximation properties for many problems, they have gained little traction in the computer graphics community.
Andreas Longva +4 more
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On Higher Order Pyramidal Finite Elements
Advances in Applied Mathematics and Mechanics, 2011In this paper we first prove a theorem on the nonexistence of pyramidal polynomial basis functions. Then we present a new symmetric composite pyrami- dal finite element which yields a better convergence than the nonsymmetric one. It has fourteen degrees of freedom and its basis functions are incomplete piece- wise triquadratic polynomials. The space of
Liu, L. +3 more
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Higher-Order Finite Element for Sandwich Plates
AIAA Journal, 1998A finite element model for the analysis of sandwich plates with laminated composites face-sheets is developed. In the model, the face-sheets are represented as ReissnerMindlin plates and therefore include shear deformation effects. The core is modelled as a three-dimensional continuum in which the through-thickness representation of the displacement ...
S. Oskooei, J. Hansen
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Electromagnetic Scattering by Isoparametric Elements of Higher Order
Computational Methods in Applied Mathematics, 2014Abstract. A boundary element method with higher order isoparametric elements allows for the simulation of scattering problems given by the electric field integral equation. This paper describes the implementation and provides striking numerical evidence of the higher order convergence rates for the approximation of the electric surface ...
Lucy Weggler +2 more
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Methods and framework for visualizing higher-order finite elements
IEEE Transactions on Visualization and Computer Graphics, 2006The finite element method is an important, widely used numerical technique for solving partial differential equations. This technique utilizes basis functions for approximating the geometry and the variation of the solution field over finite regions, or elements, of the domain.
William J. Schroeder +6 more
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Asteroid Mean Elements: Higher Order and Iterative Theories
Celestial Mechanics and Dynamical Astronomy, 1998The authors present an accurate and reliable algorithm to compute mean elements of asteroids. A satisfactory accurracy is obtained much closer to the strongest mean motion resonances. The fixed-point-based algorithm is iterative, with the first-order theory as an iteration step.
MILANI COMPARETTI, ANDREA +1 more
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