相关论文: Numerical Methods for Biomembranes: conforming sub…
In this paper, we investigate the problem of stochastic multi-level compositional optimization, where the objective function is a composition of multiple smooth but possibly non-convex functions. Existing methods for solving this problem…
Maps from a source manifold $ {\mathcal M}$ to a target manifold ${\mathcal N}$ appear in liquid crystals, colour image enhancement, texture mapping, brain mapping, and many other areas. A numerical framework to solve variational problems…
We propose numerical simulations of viscoelastic fluids based on a hybrid algorithm combining Lattice-Boltzmann models (LBM) and Finite Differences (FD) schemes, the former used to model the macroscopic hydrodynamic equations, and the…
We construct a structure preserving non-conforming finite element approximation scheme for the bi-harmonic wave maps into spheres equation. It satisfies a discrete energy law and preserves the non-convex sphere constraint of the continuous…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
This paper is devoted to the study of a novel mixed Finite Element Method for approximating the solutions of fourth order variational problems subjected to a constraint. The first problem we consider consists in establishing the convergence…
Partial differential equations (PDEs) on surfaces are fundamental to scientific computing and geometry processing. A popular approach to solving PDEs on surfaces is the finite element method (FEM), where the surface is divided into discrete…
We introduce suitable coordinate systems for pipes and their variants that allow us to transform partial differential equations (PDEs) on the pipe surfaces or in the solid pipes into computational domains with fixed limits/ranges. Such a…
Porosity-based models are a viable alternative to classical two-dimensional (2-d) Shallow water Equations (SWE) when the interaction of shallow flows with obstacles is modelled. The exact solution of the Single Porosity (SP) Riemann…
We consider a discrete-continuum model of a biomembrane with embedded particles. While the membrane is represented by a continuous surface, embedded particles are described by rigid discrete objects which are free to move and rotate in…
Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity, group sparsity, low-rank and sharp edges. It is also the basis for…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…
In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…
We present numerical experiments for geophysics electromagnetic (EM) modeling based upon high-order edge elements and supervised $h+p$ refinement approaches on massively parallel computers. Our high-order $h+p$ refinement strategy is based…
This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…
Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely…
The Wave Based Method (WBM) is a Trefftz method for the simulation of wave problems in vibroacoustics. Like other Trefftz methods, it employs a non-standard discretisation basis consisting of solutions of the partial differential equation…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical…