Related papers: Quasi-optimal mesh sequence construction through S…
We consider scalar semilinear elliptic PDEs, where the nonlinearity is strongly monotone, but only locally Lipschitz continuous. To linearize the arising discrete nonlinear problem, we employ a damped Zarantonello iteration, which leads to…
In this paper, we develop an adaptive high-order surface finite element method (FEM) incorporating the spectral deferred correction method for chain contour discretization to solve polymeric self-consistent field equations on general curved…
Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
The scaled boundary finite element method (SBFEM) is a semi-analytical computational scheme, which is based on the characteristics of the finite element method (FEM) and combines the advantages of the boundary element method (BEM). This…
To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…
We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the…
An optimization scheme using the Cell-based Smoothed Finite Element Method (CS-FEM) combined with a Genetic Algorithm (GA) framework is proposed in this paper to design shape adaptive laminated composite marine propellers. The proposed…
This paper presents a new finite difference method, called {\varphi}-FD, inspired by the {\phi}-FEM approach for solving elliptic partial differential equations (PDEs) on general geometries. The proposed method uses Cartesian grids,…
The aim of this study was to check how efficient can be smoothed finite element method (FEM) for solution of the linear fracture mechanics problems. Accuracy of stress intensity factor (SIF) computation were investigated using three types…
For adaptive mixed finite element methods (AMFEM), we first introduce the data oscillation to analyze, without the restriction that the inverse of the coefficient matrix of the partial differential equations (PDEs) is a piecewise polynomial…
The aggregated unfitted finite element method (AgFEM) is a methodology recently introduced in order to address conditioning and stability problems associated with embedded, unfitted, or extended finite element methods. The method is based…
This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of…
We use the ideas of goal-oriented error estimation and adaptivity to design and implement an efficient adaptive algorithm for approximating linear quantities of interest derived from solutions to elliptic partial differential equations…
The cost and accuracy of simulating complex physical systems using the Finite Element Method (FEM) scales with the resolution of the underlying mesh. Adaptive meshes improve computational efficiency by refining resolution in critical…
We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations. We employ analysis-suitable T-splines of arbitrary odd…
Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally…
We develop an efficient and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the regularization technique of Chen, Holst, and Xu; this technique made possible the first a…
Computational modelling offers a cost-effective and time-efficient alternative to experimental studies in biomedical engineering. In cardiac electro-mechanics, finite element method (FEM)-based simulations provide valuable insights into…
The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…