Related papers: Parallel two-scale finite element implementation o…
Functional aspects as well as the influence of integration technology on the system behavior have to be considered in the 3D integration design process of micro systems. Therefore, information from different physical domains has to be…
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…
We introduce the multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficient $a=\exp(Z)$ where $Z$ is a Gaussian random field defined by an infinite series expansion $Z(\boldsymbol{y}) =…
Cellular morphodynamics requires solving systems of coupled partial differential equations on moving bulk and surface domains, where advection-dominant transport, structure preservation, and severe mesh distortions make robust simulation…
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current…
In this work, we apply the finite element heterogeneous multiscale method to a class of dispersive first-order time-dependent Maxwell systems. For this purpose, we use an analytic homogenization result, which shows that the effective system…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…
Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome…
A dual hybrid Virtual Element scheme for plane linear elastic problems is presented and analysed. In particular, stability and convergence results have been established. The method, which is first order convergent, has been numerically…
We introduce the multivariate decomposition finite element method (MDFEM) for solving elliptic PDEs with uniform random diffusion coefficients. We show that the MDFEM can be used to reduce the computational complexity of estimating the…
Accurately depicting multiphysics interactions in interfacial systems requires computational frameworks capable of reconciling geometric adaptability with strict conservation fidelity. However, traditional spatiotemporal discretisation…
Owing to additive manufacturing techniques, a structure at millimeter length scale (macroscale) can be produced by using a lattice substructure at micrometer length scale (microscale). Such a system is called a metamaterial at the…
We propose an implementation of linear finite element method for nonlocal diffusion problem in 2D space. In the implementation, we reduce the integral from 4D to 2D which would simplify the computation significantly.
We present the implementation of a solution scheme for fluid-structure interaction problems via the finite element software library deal.II. The solution scheme is an immersed finite element method in which two independent discretizations…
We propose a parametric sampling strategy for the reduction of large-scale PDE systems with multidimensional input parametric spaces by leveraging models of different fidelity. The design of this methodology allows a user to adaptively…
In this paper, we propose a parallel solver for solving the quasi-static linear poroelasticity coupled with linear elasticity model in the Lagrange multiplier framework. Firstly, we reformulate the model into a coupling of the nearly…
In this paper, for solving a class of linear parabolic equations in rectangular domains, we have proposed an efficient Parareal exponential integrator finite element method. The proposed method first uses the finite element approximation…
A robust $hp$-adaptive finite element framework is presented for the investigation of static cracks in materials characterized by complex, pointwise density variations. Within such heterogeneous media, the equilibrium equation governed by…
The paper deals with the homogenization of deformable porous media saturated by two-component electrolytes. The model relevant to the microscopic scale describes steady states of the medium while reflecting essential physical phenomena,…
We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…