Minimization of p-Laplacian via the Finite Element Method in MATLAB

Autoři: RNDr. Ctirad Matonoha, Ph.D.
Rok vydání: 2022
Typ publikace: Konferenční příspěvek (mezinárodní konf.)
Periodikum: Large-Scale Scientific Computing
Bibliografická citace: MATONOHA, Ctirad, MOSKOVKA, A., VALDMAN, Jan. Minimization of p-Laplacian via the Finite Element Method in MATLAB. In: LIRKOV, I., MARGENOV, S., eds. Large-Scale Scientific Computing. Cham: Springer, 2022, S. 533-540. Lecture Notes in Computer Science, 13127. ISBN 978-3-030-97548-7. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-030-97549-4_61.
DOI: 10.1007/978-3-030-97549-4_61
ID: 556726

Abstrakt

Minimization of energy functionals is based on a discretization by the finite element method and optimization by the trust-region method. A key tool to an efficient implementation is a local evaluation of the approximated gradients together with sparsity of the resulting Hessian matrix. Vectorization concepts are explained for the p-Laplace problem in one and two space-dimensions.