oFEM: An object oriented finite element package for Matlab

Dudzinski, Michael; Rozgic̀, Marco; Stiemer, Marcus

doi:10.1016/j.amc.2017.11.042

Cited by 5 publications

(4 citation statements)

References 10 publications

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“…In practice, this scheme is realized by a table of points for which solutions computed by a FEM have to be evaluated. To do so quickly, an efficient point location algorithm based on a hierarchical substructuring of the finite-element mesh is implemented in the employed software oFEM [11]. In this way, the constraints of the MILP obtained after discretization are computed in advance.…”

Section: Computing Discrete States For a Basis Of The Control Spacementioning

confidence: 99%

“…All computations were carried out on a 2018 Mac mini with a 3.2 GHz Intel Core i7 CPU and 64 GB RAM. All occurring MILPs were solved by the branch-and-cut solver IBM ILOG CPLEX 12.8.0.0, and the PDE solutions needed in the preprocessing step of the model based on finite elements were obtained by employing the object-oriented software package oFEM [11]. While the IBM ILOG CPLEX can be used as a black box for solving MILPs, it also provides "callbacks", which are interfaces that can be used to include customized subroutines in the branch-and-cut process.…”

Section: Implementation Details and Computational Experimentsmentioning

confidence: 99%

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A solution framework for linear PDE-constrained mixed-integer problems

et al. 2021

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We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

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Section: Computing Discrete States For a Basis Of The Control Spacementioning

confidence: 99%

Section: Implementation Details and Computational Experimentsmentioning

confidence: 99%

A solution framework for linear PDE-constrained mixed-integer problems

et al. 2021

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“…The simulation is done using the program oFEM, an efficient implementation of the FEM in MATLAB by Dudzinski et al (2018). Meshes for the subdomains X i can be generated by any meshing tool and imported.…”

Section: Implementation Detailsmentioning

confidence: 99%

Electro-quasistatic field-simulation of biological cells using balanced domain-decomposition

Bohmelt

Kielian

Hagel

et al. 2020

COMPEL

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Purpose The purpose of this paper is to present the implementation of a balanced domain decomposition approach for the numerical simulation of large electro-quasistatic (EQS) systems in biology. The numerical scheme is analyzed and first applications are discussed. Design/methodology/approach The scheme is based on a finite element discretization of the individual domains obtained by decomposition and a physically consistent inter-domain coupling realized via Robin boundary conditions. The proposed algorithms can efficiently be implemented on a highly parallelized computing grid. Findings The feasibility and applicability of the method is proven. Further, a couple of technical details are found that increase the efficiency of the method. Originality/value The presented method offers an enhanced geometrical flexibility and extensibility to simulate larger cell systems with higher model resolution compared to other methods presented in the literature. The presented analysis provides an understanding of the balanced coupling scheme for large EQS systems.

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“…Currently, there are many software packages developed for utilizing FEM to solve various scientific and engineering problems, while the development of software and library packages for the S-FEM is still in progress [30]. Current S-FEM software packages are mostly implemented in C++ and Fortran.…”

Section: Introductionmentioning

confidence: 99%

epSFEM: A Julia-Based Software Package of Parallel Incremental Smoothed Finite Element Method (S-FEM) for Elastic-Plastic Problems

et al. 2022

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In this paper, a parallel Smoothed Finite Element Method (S-FEM) package epSFEM using incremental theory to solve elastoplastic problems is developed by employing the Julia language on a multicore CPU. The S-FEM, a new numerical method combining the Finite Element Method (FEM) and strain smoothing technique, was proposed by Liu G.R. in recent years. The S-FEM model is softer than the FEM model for identical grid structures, has lower sensitivity to mesh distortion, and usually produces more accurate solutions and a higher convergence speed. Julia, as an efficient, user-friendly and open-source programming language, balances computational performance, programming difficulty and code readability. We validate the performance of the epSFEM with two sets of benchmark tests. The benchmark results indicate that (1) the calculation accuracy of epSFEM is higher than that of the FEM when employing the same mesh model; (2) the commercial FEM software requires 10,619 s to calculate an elastoplastic model consisting of approximately 2.45 million triangular elements, while in comparison, epSFEM requires only 5876.3 s for the same computational model; and (3) epSFEM executed in parallel on a 24-core CPU is approximately 10.6 times faster than the corresponding serial version.

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oFEM: An object oriented finite element package for Matlab

Cited by 5 publications

References 10 publications

A solution framework for linear PDE-constrained mixed-integer problems

A solution framework for linear PDE-constrained mixed-integer problems

Electro-quasistatic field-simulation of biological cells using balanced domain-decomposition

epSFEM: A Julia-Based Software Package of Parallel Incremental Smoothed Finite Element Method (S-FEM) for Elastic-Plastic Problems

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