Alfarisy, Dewangga and Zuhal, Lavi and Ortiz, Michael and Cirak, Fehmi and Febrianto, Eky (2024) Point collocation with mollified piecewise polynomial approximants for high-order partial differential equations. International Journal for Numerical Methods in Engineering, 125 (18): e7548. ISSN 0029-5981
AI Summary:
The solution approximation for partial differential equations (PDEs) can be substantially improved using smooth basis functions. The recently introduced mollified basis functions are constructed through mollification, or convolution, of cell-wise defined piecewise polynomials with a smooth mollifier of certain characteristics.AI Topics:
The solution approximation for partial differential equations (PDEs) can be substantially improved using smooth basis functions. The recently introduced mollified basis functions are constructed through mollification, or convolution, of cell-wise defined piecewise polynomials with a smooth mollifier of certain characteristics. The properties of the mollified basis functions are governed by the order of the piecewise functions and the smoothness of the mollifier. In this work, we exploit the high-order and high-smoothness properties of the mollified basis functions for solving PDEs through the point collocation method. The basis functions are evaluated at a set of collocation points in the domain. In addition, boundary conditions are imposed at a set of boundary collocation points distributed over the domain boundaries. To ensure the stability of the resulting linear system of equations, the number of collocation points is set larger than the total number of basis functions. The resulting linear system is overdetermined and is solved using the least square technique. The presented numerical examples confirm the convergence of the proposed approximation scheme for Poisson, linear elasticity, and biharmonic problems. We study in particular the influence of the mollifier and the spatial distribution of the collocation points.
Alfarisy, Dewangga
Author
Alfarisy, Dewangga and Zuhal, Lavi and Ortiz, Michael and Cirak, Fehmi and Febrianto, Eky (2024) Point collocation with mollified piecewise polynomial approximants for high-order partial differential equations. International Journal for Numerical Methods in Engineering, 125 (18): e7548. ISSN 0029-5981
See full publications listZuhal, Lavi
Author
Alfarisy, Dewangga and Zuhal, Lavi and Ortiz, Michael and Cirak, Fehmi and Febrianto, Eky (2024) Point collocation with mollified piecewise polynomial approximants for high-order partial differential equations. International Journal for Numerical Methods in Engineering, 125 (18): e7548. ISSN 0029-5981
See full publications listOrtiz, Michael
Author
Alfarisy, Dewangga and Zuhal, Lavi and Ortiz, Michael and Cirak, Fehmi and Febrianto, Eky (2024) Point collocation with mollified piecewise polynomial approximants for high-order partial differential equations. International Journal for Numerical Methods in Engineering, 125 (18): e7548. ISSN 0029-5981
See full publications listCirak, Fehmi
Author
Alfarisy, Dewangga and Zuhal, Lavi and Ortiz, Michael and Cirak, Fehmi and Febrianto, Eky (2024) Point collocation with mollified piecewise polynomial approximants for high-order partial differential equations. International Journal for Numerical Methods in Engineering, 125 (18): e7548. ISSN 0029-5981
Febrianto, Eky and Šístek, Jakub and Kůs, Pavel and Kecman, Matija and Cirak, Fehmi (2024) A three-grid high-order immersed finite element method for the analysis of CAD models. Computer-Aided Design, 173: 103730. ISSN 0010-4485
Sun, Fuzheng and Febrianto, Eky and Fernando, Heshan and Butler, Liam J. and Cirak, Fehmi and Hoult, Neil A. (2023) Data-informed statistical finite element analysis of rail buckling. Computers and Structures, 289: 107163. ISSN 0045-7949
See full publications listFebrianto, Eky
Author
Wiragunarsa, I.M. and Zuhal, L.R. and Dirgantara, T. and Putra, I.S. and Febrianto, E. (2024) Total Lagrangian smoothed particle hydrodynamics with an improved bond-based deformation gradient for large strain solid dynamics. Journal of Computational Physics, 518: 113309. ISSN 0021-9991
Alfarisy, Dewangga and Zuhal, Lavi and Ortiz, Michael and Cirak, Fehmi and Febrianto, Eky (2024) Point collocation with mollified piecewise polynomial approximants for high-order partial differential equations. International Journal for Numerical Methods in Engineering, 125 (18): e7548. ISSN 0029-5981
Febrianto, Eky and Šístek, Jakub and Kůs, Pavel and Kecman, Matija and Cirak, Fehmi (2024) A three-grid high-order immersed finite element method for the analysis of CAD models. Computer-Aided Design, 173: 103730. ISSN 0010-4485
See full publications listAvailable under License Creative Commons Attribution.
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