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This paper deals with a simple and straightforward procedure for automatic generation of finite-element or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Besides the equation of the boundary, the generated meshes…
Algorithms that promise to leverage resources of quantum computers efficiently to accelerate the finite element method have emerged. However, the finite element method is usually incorporated into a high-level numerical scheme which allows…
When using the finite element method (FEM) in inverse problems, its discretization error can produce parameter estimates that are inaccurate and overconfident. The Bayesian finite element method (BFEM) provides a probabilistic model for the…
This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle-triangle mapping proposed in the conference note [21]. Here, we provide some new insights into the…
The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the…
In the current practices of both industry and academia, the convergence and accuracy of finite element calculations are closely related to the methods and quality of mesh generation. For years, the research on high-quality mesh generation…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
The finite element method has become a preeminent simulation technique in electromagnetics. For problems involving anisotropic media and metamaterials, proper algorithms should be developed. It has been proved that discretizing in quadratic…
This paper introduces a new weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This method, called WG-FEM, is designed by using a discrete weak gradient operator applied to discontinuous…
Several authors have employed Finite Element Analysis (FEA) for stress and strain analysis in orthopaedic biomechanics. Unfortunately, the use of three-dimensional models is time consuming and consequently the number of analysis to be…
The approximation properties of a quadratic iso-parametric finite element method for a typical cavitation problem in nonlinear elasticity are analyzed. More precisely, (1) the finite element interpolation errors are established in terms of…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
Finite Element mesh generation remains an important issue for patient specific biomechanical modeling. While some techniques make automatic mesh generation possible, in most cases, manual mesh generation is preferred for better control over…
Finite Element mesh generation remains an important issue for patient specific biomechanical modeling. While some techniques make automatic mesh generation possible, in most cases, manual mesh generation is preferred for better control over…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…
This work illustrates the possibility to apply the Fast Fourier Transformation to obtain the integrals of the Boundary Element Method (BEM) on arbitrary shapes. The procedure is inspired by the technique used with great success within the…
We consider the vertex-centered finite volume method with first-order conforming ansatz functions. The adaptive mesh-refinement is driven by the local contributions of the weighted-residual error estimator. We prove that the adaptive…
This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection…