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In recent years, the immersed finite element methods (IFEM) introduced in \cite{Li2003}, \cite{Li2004} to solve elliptic problems having an interface in the domain due to the discontinuity of coefficients are getting more attentions of…
This paper introduces the Scaled Coordinate Transformation Boundary Element Method (SCTBEM), a novel boundary-type method for solving 3D potential problems. To address the challenges of applying the Boundary Element Method (BEM) to complex…
To solve large-scale or high-resolution topology optimization problem, a novel algorithm is developed based on modified bi-directional evolutionary structure optimization (BESO) and extended finite element method (XFEM). Within XFEM, a set…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…
Recent work in on-line Statistical Process Control (SPC) of manufactured 3-dimensional (3-D) objects has been proposed based on the estimation of the spectrum of the Laplace-Beltrami (LB) operator, a differential operator that encodes the…
This paper presents a novel exact finite element formulation of quasi-3D beam for high-fidelity analysis of functionally graded sandwich beams. Unlike conventional displacement-based elements that rely on approximate interpolation functions…
Obtaining high-quality particle distributions for stable and accurate particle-based simulations poses significant challenges, especially for complex geometries. We introduce a preprocessing technique for 2D and 3D geometries, optimized for…
Three different displacement based finite element formulations over arbitrary polygons are studied in this paper. The formulations considered are: the conventional polygonal finite element method (FEM) with Laplace interpolants, the…
The combination of Finite Element Method (FEM) simulation and experimental photo-elasticity provides both qualitative and quantitative information about the stress field in a polymer composite and particularly along the fibre-matrix…
Particle breakage due to collisional interactions plays a vital role in the development of several phenomena in science and engineering. The nonlinear collisional breakage equations (NCBEs) are a significant set of equations in this…
We propose an energy-stable parametric finite element method (ES-PFEM) to discretize the motion of a closed curve under surface diffusion with an anisotropic surface energy $\gamma(\theta)$ -- anisotropic surface diffusion -- in two…
As the capabilities of additive manufacturing techniques increase, topology optimization provides a promising approach to design geometrically sophisticated structures which can be directly manufactured. Traditional topology optimization…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
The extended finite element method (XFEM) was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to be split by a discontinuity, strong…
We present in this paper a rigorous theoretical framework to show stability, convergence and accuracy of improved edge-based and face-based smoothed finite element methods (bESFEM and bFS-FEM) for nearly-incompressible elasticity problems.…
We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted piecewise…
The presented paper concentrates on the boundary element method (BEM) for the heat equation in three spatial dimensions. In particular, we deal with tensor product space-time meshes allowing for quadrature schemes analytic in time and…
A new finite element method (FEM) using meshes that do not necessarily align with the interface is developed for two- and three-dimensional anisotropic elliptic interface problems with nonhomogeneous jump conditions. The degrees of freedom…
An isogeometric boundary element method (BEM) is presented to solve scattering problems in an isotropic homogeneous medium. We consider wave problems governed by the scalar wave equation as in acoustics and the Lam\'e-Navier equations for…