Related papers: Shape Optimization using the Finite Element Method…
We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…
We present a methodical procedure for topology optimization under uncertainty with multi-resolution finite element models. We use our framework in a bi-fidelity setting where a coarse and a fine mesh corresponding to low- and…
Accurately depicting multiphysics interactions in interfacial systems requires computational frameworks capable of reconciling geometric adaptability with strict conservation fidelity. However, traditional spatiotemporal discretisation…
We present an improved method for topology optimization with both adaptive mesh refinement and derefinement. Since the total volume fraction in topology optimization is usually modest, after a few initial iterations the domain of…
We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…
Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an…
Modern product design in the engineering domain is increasingly driven by computational analysis including finite-element based simulation, computational optimization, and modern data analysis techniques such as machine learning. To apply…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the…
We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…
We present an optimization procedure for generic polygonal or polyhedral meshes, tailored for the Virtual Element Method (VEM). Once the local quality of the mesh elements is analyzed through a quality indicator specific to the VEM, groups…
Computing the stiffness matrix for the finite element discretization of the nonlocal Laplacian on unstructured meshes is difficult, because the operator is nonlocal and can even be singular. In this paper, we focus on the $C^0$-piecewise…
In this paper, we present a robust and efficient unfitted concurrent multiscale method for continuum-continuum coupling, based on the Cut Finite Element Method (CutFEM). The computational domain is defined using approximate signed distance…
This work develops an algorithm for PDE-constrained shape optimization based on Lipschitz transformations. Building on previous work in this field, the $p$-Laplace operator is utilized to approximate a descent method for Lipschitz shapes.…
Existing implementations of gradient-based optimisation methods typically assume that the problem is posed in Euclidean space. When solving optimality problems on function spaces, the functional derivative is then inaccurately represented…
This work surveys an r-adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…
A new density field representation technique called the Bezier skeleton explicit density (BSED) representation scheme for topology optimization of stretchable metamaterials under finite deformation is proposed for the first time. The…
This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order…