Coupling finite element method with meshless finite difference method by means of approximation constraints
The novel coupling technique applied to standard Finite Element and meshless Finite Difference Methods is presented in this paper. The problem domain is a priori partitioned into a set of disjoint subdomains, which are subsequently discretized using frameworks typical for the finite element method o...
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| Vydané v: | Computers & mathematics with applications (1987) Ročník 142; s. 208 - 224 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Ltd
15.07.2023
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| ISSN: | 0898-1221, 1873-7668 |
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| Abstract | The novel coupling technique applied to standard Finite Element and meshless Finite Difference Methods is presented in this paper. The problem domain is a priori partitioned into a set of disjoint subdomains, which are subsequently discretized using frameworks typical for the finite element method or the meshless finite difference method. The constraints problem, based on the least square approach, is established whose solution yields combinations of degrees of freedom in subdomains that determine the global approximation field, continuous in the entire domain. The constraints problem has the matrix-type form and requires solving the strongly singular system of equations. The appropriate technique is presented to find the complete solution in the form of a hyperplane in the space of degrees of freedom. The same method is applied to enforce the boundary conditions in the meshless subdomains. The proposed approach is illustrated with several 2D examples, including the standard Poisson's problem and selected elasticity and thermo-elasticity problems. In each case, it is shown that the novel method of coupling FEM and MFDM is effective since it provides an accurate and continuous solution in the entire domain.
•Domain partitioning does not significantly decrease accuracy of the final solution.•Finite element and meshless finite difference methods are coupled in one domain.•Various discretization and approximation parameters lead to the continuous final solution.•Convergence rates on multi-region domains correspond to those obtained on homogeneous ones. |
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| AbstractList | The novel coupling technique applied to standard Finite Element and meshless Finite Difference Methods is presented in this paper. The problem domain is a priori partitioned into a set of disjoint subdomains, which are subsequently discretized using frameworks typical for the finite element method or the meshless finite difference method. The constraints problem, based on the least square approach, is established whose solution yields combinations of degrees of freedom in subdomains that determine the global approximation field, continuous in the entire domain. The constraints problem has the matrix-type form and requires solving the strongly singular system of equations. The appropriate technique is presented to find the complete solution in the form of a hyperplane in the space of degrees of freedom. The same method is applied to enforce the boundary conditions in the meshless subdomains. The proposed approach is illustrated with several 2D examples, including the standard Poisson's problem and selected elasticity and thermo-elasticity problems. In each case, it is shown that the novel method of coupling FEM and MFDM is effective since it provides an accurate and continuous solution in the entire domain.
•Domain partitioning does not significantly decrease accuracy of the final solution.•Finite element and meshless finite difference methods are coupled in one domain.•Various discretization and approximation parameters lead to the continuous final solution.•Convergence rates on multi-region domains correspond to those obtained on homogeneous ones. |
| Author | Jaśkowiec, Jan Milewski, Sławomir |
| Author_xml | – sequence: 1 givenname: Jan orcidid: 0000-0002-4047-1339 surname: Jaśkowiec fullname: Jaśkowiec, Jan email: jan.jaskowiec@pk.edu.pl – sequence: 2 givenname: Sławomir orcidid: 0000-0003-4967-9061 surname: Milewski fullname: Milewski, Sławomir email: slawomir.milewski@pk.edu.pl |
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| Keywords | Error analysis Finite Element Method Thermo-elastic problems Constraints problem Meshless Finite Difference Method Coupling methods |
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| SubjectTerms | Constraints problem Coupling methods Error analysis Finite Element Method Meshless Finite Difference Method Thermo-elastic problems |
| Title | Coupling finite element method with meshless finite difference method by means of approximation constraints |
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