scholarly journals A Numerical Simulator Based on Finite Element Method for Diffusion-Advection-Reaction Equation in High Contrast Domains

2021 ◽  
Author(s):  
Hani Akbari
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computational Cost ◽  
Nonlinear Parabolic Equations ◽  
High Contrast ◽  
Nonlinear Parabolic ◽  
2D And 3D ◽  
Reaction Problem ◽  
Numerical Simulator ◽  
Element Method

Implementation of finite element method (FEM) needs special cares, particularly for essential boundary conditions that have an important effect on symmetry and number of unknowns in the linear systems. Moreover, avoiding numerical integration and using (off-line) calculated element integrals decrease the computational cost significantly. In this chapter we briefly present theoretical topics of FEM. Instead we focus on what is important (and how) to carefully implement FEM for equations that can be the core of a numerical simulator for a diffusion–advection-reaction problem. We consider general 2D and 3D domains, high contrast and heterogeneous diffusion coefficients and generalize the method to nonlinear parabolic equations. Although we use Matlab codes to simplify the explanation of the proposed method, we have implemented it in C++ to reveal the efficiency and examples are presented to admit it.

Development of SFEM-Pre: A Novel Preprocessor for Model Creation for the Smoothed Finite Element Method

2019 ◽  
Vol 17 (02) ◽  
pp. 1845002 ◽  
Author(s):  
J. F. Zhang ◽  
R. P. Niu ◽  
Y. F. Zhang ◽  
C. Q. Wang ◽  
M. Li ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Complex Geometry ◽  
Three Dimensional ◽  
Efficient Computation ◽  
Practical Engineering ◽  
Smoothed Finite Element Method ◽  
2D And 3D ◽  
First Time ◽  
Element Method

Smoothed finite element method (S-FEM) is a new general numerical method which has been applied to solve various practical engineering problems. It combines standard finite element method (FEM) and meshfree techniques based on the weaken-weak (W2) formulation. This project, for the first time, develops a preprocessor software package SFEM-Pre for creating types of two-dimensional (2D) and three-dimensional (3D) S-FEM models following strictly the S-FEM theory. Because the software architecture of our 3D processor is the same as our 2D preprocessor, we will mainly introduce the 2D preprocessor in terms of software design for easier description, but the examples will include both 2D and 3D cases to fully demonstrate and validate the whole preprocessor of S-FEM. Our 2D preprocessor package is equipped with a graphical user interface (GUI) for easy use, and with a connectivity database for efficient computation. Schemes are developed for not only automatically meshes the problem domains using our GUI, but also accepts various geometry files made available from some existing commercial software packages, such as ABAQUS®and HyperMesh®. In order to improve the efficiency of our preprocessor, a parallel triangulation mesh generator has also been developed based on the advancing front technique (AFT) to create triangular meshes for complex geometry, and at the same time to create six types of connectivity needed for various S-FEM models. In addition, a database is implemented in our code to record all these connectivity to avoid duplicated calculation. Finally, intensive numerical experiments are conducted to validate the efficiency, accuracy and stability of our preprocessor codes. It is shown that with our preprocessor, an S-FEM can be created automatically without much human intervention for geometry of arbitrary complexity.

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