Interpolation with restrictions -- role of the boundary conditions and individual restrictions

Valášek, Jan, and Sváček, Petr. "Interpolation with restrictions -- role of the boundary conditions and individual restrictions." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2023. 281-292. <http://eudml.org/doc/299026>.

@inProceedings{Valášek2023,
abstract = {The contribution deals with the remeshing procedure between two computational finite element meshes. The remeshing represented by the interpolation of an approximate solution onto a new mesh is needed in many applications like e.g. in aeroacoustics, here we are particularly interested in the numerical flow simulation of a gradual channel collapse connected with a~severe deterioration of the computational mesh quality. Since the classical Lagrangian projection from one mesh to another is a dissipative method not respecting conservation laws, a conservative interpolation method introducing constraints is described. The constraints have form of Lagrange multipliers enforcing conservation of desired flow quantities, like e.g. total fluid mass, flow kinetic energy or flow potential energy. Then the interpolation problem turns into an error minimization problem, such that the resulting quantities of proposed interpolation satisfy these physical properties while staying as close as possible to the results of Lagrangian interpolation in the L2 norm. The proposed interpolation scheme does not impose any restrictions on mesh generation process and it has a relatively low computational cost. The implementation details are discussed and test cases are shown.},
author = {Valášek, Jan, Sváček, Petr},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {interpolation; Lagrange multiplier; Lagrange projection},
location = {Prague},
pages = {281-292},
publisher = {Institute of Mathematics CAS},
title = {Interpolation with restrictions -- role of the boundary conditions and individual restrictions},
url = {http://eudml.org/doc/299026},
year = {2023},
}

TY - CLSWK
AU - Valášek, Jan
AU - Sváček, Petr
TI - Interpolation with restrictions -- role of the boundary conditions and individual restrictions
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2023
CY - Prague
PB - Institute of Mathematics CAS
SP - 281
EP - 292
AB - The contribution deals with the remeshing procedure between two computational finite element meshes. The remeshing represented by the interpolation of an approximate solution onto a new mesh is needed in many applications like e.g. in aeroacoustics, here we are particularly interested in the numerical flow simulation of a gradual channel collapse connected with a~severe deterioration of the computational mesh quality. Since the classical Lagrangian projection from one mesh to another is a dissipative method not respecting conservation laws, a conservative interpolation method introducing constraints is described. The constraints have form of Lagrange multipliers enforcing conservation of desired flow quantities, like e.g. total fluid mass, flow kinetic energy or flow potential energy. Then the interpolation problem turns into an error minimization problem, such that the resulting quantities of proposed interpolation satisfy these physical properties while staying as close as possible to the results of Lagrangian interpolation in the L2 norm. The proposed interpolation scheme does not impose any restrictions on mesh generation process and it has a relatively low computational cost. The implementation details are discussed and test cases are shown.
KW - interpolation; Lagrange multiplier; Lagrange projection
UR - http://eudml.org/doc/299026
ER -