Details
| Original language | English |
|---|---|
| Article number | 104353 |
| Journal | Finite Elements in Analysis and Design |
| Volume | 249 |
| Early online date | 14 May 2025 |
| Publication status | E-pub ahead of print - 14 May 2025 |
Abstract
Gradient-enhanced regularization is a frequently utilized method for addressing numerical issues in material modeling. As a consequence of the regularization scheme, Laplacian terms will emerge in the strong form of evolution equations for additional field variables, also called internal variables. In a series of previous works, the Neighbored Element Method (NEM) was presented as a combination of the Finite Element Method and a generalized finite difference scheme with a weighted least-square method to approximate the Laplacian. The objective is the efficient solution of the total system of equations containing Laplacian and gradient terms. The systems of equations used with the NEM have a similar structure to, e.g., the heat and diffusion equation. In this study, the NEM is evaluated even further, in comparison to a well-established FEM routine with respect to accuracy and computational efficiency through investigating a chemo-thermo-mechanical system. It is demonstrated that the accuracy improves with a reduction in element size and, for an appropriate mesh, the relative average error is below 1%. These highly accurate solutions can be achieved with a notable reduction in computational time and memory cost of up two orders of magnitude, for approximately 620000 nodes with five degrees of freedom per node. This new technique can be applied to arbitrary solid finite element types and/or irregular meshes.
Keywords
- Coupled problems, Finite Difference Method, Finite Element Method, Numerical simulation
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Engineering(all)
- General Engineering
- Computer Science(all)
- Computer Graphics and Computer-Aided Design
- Mathematics(all)
- Applied Mathematics
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In: Finite Elements in Analysis and Design, Vol. 249, 104353, 07.2025.
Research output: Contribution to journal › Review article › Research › peer review
}
TY - JOUR
T1 - Computational efficiency and accuracy of the Neighbored Element Method
AU - Rudolf, Tobias
AU - Klempt, Felix
AU - Kök, Hüray Ilayda
AU - Soleimani, Meisam
AU - Jantos, Dustin Roman
AU - Junker, Philipp
N1 - Publisher Copyright: © 2025 The Authors
PY - 2025/5/14
Y1 - 2025/5/14
N2 - Gradient-enhanced regularization is a frequently utilized method for addressing numerical issues in material modeling. As a consequence of the regularization scheme, Laplacian terms will emerge in the strong form of evolution equations for additional field variables, also called internal variables. In a series of previous works, the Neighbored Element Method (NEM) was presented as a combination of the Finite Element Method and a generalized finite difference scheme with a weighted least-square method to approximate the Laplacian. The objective is the efficient solution of the total system of equations containing Laplacian and gradient terms. The systems of equations used with the NEM have a similar structure to, e.g., the heat and diffusion equation. In this study, the NEM is evaluated even further, in comparison to a well-established FEM routine with respect to accuracy and computational efficiency through investigating a chemo-thermo-mechanical system. It is demonstrated that the accuracy improves with a reduction in element size and, for an appropriate mesh, the relative average error is below 1%. These highly accurate solutions can be achieved with a notable reduction in computational time and memory cost of up two orders of magnitude, for approximately 620000 nodes with five degrees of freedom per node. This new technique can be applied to arbitrary solid finite element types and/or irregular meshes.
AB - Gradient-enhanced regularization is a frequently utilized method for addressing numerical issues in material modeling. As a consequence of the regularization scheme, Laplacian terms will emerge in the strong form of evolution equations for additional field variables, also called internal variables. In a series of previous works, the Neighbored Element Method (NEM) was presented as a combination of the Finite Element Method and a generalized finite difference scheme with a weighted least-square method to approximate the Laplacian. The objective is the efficient solution of the total system of equations containing Laplacian and gradient terms. The systems of equations used with the NEM have a similar structure to, e.g., the heat and diffusion equation. In this study, the NEM is evaluated even further, in comparison to a well-established FEM routine with respect to accuracy and computational efficiency through investigating a chemo-thermo-mechanical system. It is demonstrated that the accuracy improves with a reduction in element size and, for an appropriate mesh, the relative average error is below 1%. These highly accurate solutions can be achieved with a notable reduction in computational time and memory cost of up two orders of magnitude, for approximately 620000 nodes with five degrees of freedom per node. This new technique can be applied to arbitrary solid finite element types and/or irregular meshes.
KW - Coupled problems
KW - Finite Difference Method
KW - Finite Element Method
KW - Numerical simulation
UR - http://www.scopus.com/inward/record.url?scp=105004813819&partnerID=8YFLogxK
U2 - 10.1016/j.finel.2025.104353
DO - 10.1016/j.finel.2025.104353
M3 - Review article
AN - SCOPUS:105004813819
VL - 249
JO - Finite Elements in Analysis and Design
JF - Finite Elements in Analysis and Design
SN - 0168-874X
M1 - 104353
ER -