The presented article contains a 2D mesh generation routine optimized with the Metropolis algorithm. The procedure enables to produce meshes with a prescribed size h of elements. These finite element meshes can serve as standard discrete patterns for the Finite Element Method (FEM). Appropriate meshes together with the FEM approach constitute an effective tool to deal with differential problems...

This study presents a new procedure based on Artificial Neural Network (ANN) for identification of double cracks in Functionally Graded Beams (FGBs). A cantilever beam is modeled using Finite Element Method (FEM) for analyzing a double-cracked FGB and evaluation of its first four natural frequencies for different cracks depths and locations. The obtained FEM results are verified against availab...

Based on a geometric discretization scheme for Maxwell equations, we unveil a mathematical transformation between the electric field intensity E and the magnetic field intensity H, denoted as Galerkin duality. Using Galerkin duality and discrete Hodge operators, we construct two system matrices, [XE ] (primal formulation) and [XH ] (dual formulation) respectively, that discretize the second-ord...

For solving electroencephalographic forward problem, coupled method of finite element method FEM and fast moving least square reproducing kernel method FMLSRKM which is a kind of meshfree method is proposed. Current source modeling for FEM is complicated, so source region is analyzed usingmeshfreemethod. First order of shape function is used for FEM and second order for FMLSRKM because FMLSRKM ...

The spectral element method (SEM) is a high order numerical method for solving partial differential equations that inherits the accuracy of spectral methods and the geometrical flexibility of the finite element method. These lectures provide an introduction to the SEM for graduate students in Earth science. The construction of the method is described for a model problem in 1D and 2D. The elemen...

This paper presents an estimation technique using the Kalman filter finite element method ( KFFEM ). Estimation value that is not observed is estimated by KF-FEM, which is the combination method of the Kalman filter and the finite element method. The Kalman filter is employed for the solution of time series analysis and the finite element method is space analysis. In this paper the shallow wate...

A new method called Expanded Cholesky Method (ECM) is proposed in this paper. The method can be used to decompose sparse symmetric non-positive-definite finite element (FEM) matrices. There are some advantages of the ECM, such as low storage, simplicity and easy parallelization. Based on the method, multifrontal (MF) algorithm is applied in non-positive-definite FEM computation. Numerical resul...

Hybrid FEM/MoM methods combine the finite element method (FEM) and the method of moments (MoM) to model inhomogeneous unbounded problems. These two methods are coupled by enforcing field continuity on the boundary that separates the FEM and MoM regions. There are three ways of formulating hybrid FEM/MoM methods: outward-looking formulations, inward-looking formulations and combined formulations...

This paper presents a voxel-based biomechanical model for muscle deformation using finite element method (FEM) and volume graphics. Hierarchical voxel meshes are reconstructed from filtered segmented muscle images followed by FEM simulation and volume rendering. Physiological muscle force is considered and linear elastic muscle models for both static and dynamic cases are simulated by FEM. Voxe...