Related papers: Geometrical discretisations for unfitted finite el…
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…
This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…
We present a new finite element method, called $\phi$-FEM, to solve numerically elliptic partial differential equations with natural (Neumann or Robin) boundary conditions using simple computational grids, not fitted to the boundary of the…
In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…
This paper proposes a novel discretization workflow for contact problems in which the discretization of the contact interface is decoupled from that of the bulk domain. This separation enables independently tailored meshes for the contact…
We present a simple direct discretization for functionals used in the variational mesh generation and adaptation. Meshing functionals are discretized on simplicial meshes and the Jacobian matrix of the continuous coordinate transformation…
We present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate a given function, an auxiliary function with greater smoothness properties is defined which…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
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…
In many applications, thin shell-like structures are integrated within or attached to volumetric bodies. This includes reinforcements placed in soft matrix material in lightweight structure design, or hollow structures that are partially or…
In this paper we develop automatic shape differentiation techniques for unfitted discretisations and link these to recent advances in shape calculus for unfitted methods. We extend existing analytic shape calculus results to the case where…
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…
We develop a stabilized cut discontinuous Galerkin framework for the numerical solution of el- liptic boundary value and interface problems on complicated domains. The domain of interest is embedded in a structured, unfitted background mesh…
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. We consider a new unfitted finite element method…
We present a generic algorithm for numbering and then efficiently iterating over the data values attached to an extruded mesh. An extruded mesh is formed by replicating an existing mesh, assumed to be unstructured, to form layers of…
Operator products occur naturally in a range of regularized boundary integral equation formulations. However, while a Galerkin discretisation only depends on the domain space and the test (or dual) space of the operator, products require a…
The immersed boundary (IB) method is a non-body conforming approach to fluid-structure interaction (FSI) that uses an Eulerian description of the momentum, viscosity, and incompressibility of a coupled fluid-structure system and a…
In this paper, we discuss the solution of certain matrix-valued partial differential equations. Such PDEs arise, for example, when constructing a Riemannian contraction metric for a dynamical system given by an autonomous ODE. We develop…