Related papers: A robust and scalable unfitted adaptive finite ele…
In this paper, we consider the problem of piecewise affine abstraction of nonlinear systems, i.e., the overapproximation of its nonlinear dynamics by a pair of piecewise affine functions that "includes" the dynamical characteristics of the…
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…
Convergence failure and slow convergence rates are among the biggest challenges with solving the system of non-linear equations numerically. Although mitigated, such issues still linger when using strictly small time steps and…
This paper considers the scattering of a time-harmonic acoustic plane wave by an elastic body with an unbounded periodic surface. The original problem can be confined to the analysis of the fields in one periodic cell. With the help of the…
In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous…
Implicit solvers present strong limitations when used on supercomputing facilities and in particular for adaptive mesh-refinement codes. We present a new method for implicit adaptive time-stepping on adaptive mesh refinement-grids. We…
In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…
Implicit time integration is key to robustly simulating stiff materials and large deformations, but its performance is often dominated by repeatedly solving large linear systems. Adaptive coarsening can reduce this cost by concentrating…
In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite…
Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…
We present a hybrid mimetic finite-difference and virtual element formulation for coupled single-phase poromechanics on unstructured meshes. The key advantage of the scheme is that it is convergent on complex meshes containing highly…
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…
This paper presents the development and analysis of an asymptotically compatible (AC) unfitted finite element method for one-dimensional nonlocal elliptic interface problems. The proposed method achieves optimal error estimates through…
This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…
Pixel- and voxel-based representations of microstructures obtained from tomographic imaging methods is an established standard in computational materials science. The corresponding highly resolved, uniform discretitization in numerical…
This paper uses the HCT finite element method and mesh adaptation technology to solve the nonlinear plate bending problem and conducts error analysis on the iterative method, including a priori and a posteriori error estimates. Our…
The paper is concerned with the adaptive finite element solution of linear elliptic differential equations using equidistributing meshes. A strategy is developed for defining this type of mesh based on residual-based a posteriori error…
We present an adaptive variational procedure for unstructured meshes to capture fluid-fluid interfaces in two-phase flows. The two phases are modeled by the phase-field finite element formulation, which involves the conservative Allen-Cahn…
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the…
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…