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We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear…
A parameterization strategy for molecular models on the basis of force fields is proposed, which allows a rapid development of models for small molecules by using results from quantum mechanical (QM) ab initio calculations and thermodynamic…
Problems with localized nonhomogeneous material properties arise frequently in many applications and are a well-known source of difficulty in numerical simulations. In certain applications (including additive manufacturing), the physics of…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
In this contribution we present how to obtain explicit state space models in port-Hamiltonian form when a mixed finite element method is applied to a linear mechanical system with non-uniform boundary conditions. The key is to express the…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
In this chapter we examine reduced order techniques for geometrical parametrized heat exchange systems, Poisson, and flows based on Stokes, steady and unsteady incompressible Navier-Stokes and Cahn-Hilliard problems. The full order finite…
The finite element method is one of the widely employed numerical techniques in electrical engineering for the study of electric and magnetic fields. When applied to the moving conductor problems, the finite element method is known to have…
In this paper, we present and validate a simple adaptive surface remeshing technique to transfer history dependent variables from an old distorting mesh to a new mesh during finite element simulations of elastic surface deformation. This…
The peridynamic theory brings advantages in dealing with discontinuities, dynamic loading, and non-locality. The integro-differential formulation of peridynamics poses challenges to numerical solutions of complicated and practical problems.…
We consider problems related to initial meshing and adaptive mesh refinement for the electromagnetic simulation of various structures. The quality of the initial mesh and the performance of the adaptive refinement are of great importance…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…
The dynamical and stationary behaviors of a fourth-order equation in the unit ball with clamped boundary conditions and a singular reaction term are investigated. The equation arises in the modeling of microelectromechanical systems (MEMS)…
Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…
While doing electromagnetic analysis using FEM (Finite element method), if we can implement the underlying symmetric nature of the problem, there will be significant reduction in the computational cost. Symmetric nature of the problem can…
The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…
Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they…
This paper introduces an approach to decoupling singularly perturbed boundary value problems for fourth-order ordinary differential equations that feature a small positive parameter $\epsilon$ multiplying the highest derivative. We…
In recent years, there has been a growing interest in understanding complex microstructures and their effect on macroscopic properties. In general, it is difficult to derive an effective constitutive law for such microstructures with…
We consider basic and easily extendible transport formulations for lithium batteries consisting of an anode (Li-foil), a separator (polymer electrolyte), and a composite cathode (composed of electrolyte and intercalation particles). Our…