Related papers: A High-Order Discretization Scheme for Surface Int…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
We study stochastic optimization from a joint continuous-discrete point of view. Starting from a second-order stochastic differential equation interpreted as a noisy accelerated gradient flow, we discretize the dynamics by a fully implicit…
The sparse interferometric coverage of the Event Horizon Telescope (EHT) poses a significant challenge for both reconstruction and model fitting of black-hole images. PRIMO is a new principal components analysis-based algorithm for image…
Finite difference method was extended to unstructured meshes to solve Euler equations. The spatial discretization is made of two steps. First, numerical fluxes are computed at the middle point of each edge with high order accuracy. In this…
Over the last ten years blind source separation (BSS) has become a prominent processing tool in the study of human electroencephalography (EEG). Without relying on head modeling BSS aims at estimating both the waveform and the scalp spatial…
Quantitative phase field models have been extensively used to study the solidification behavior of alloys under different conditions. However, a longstanding challenge of phase field models is the directional bias caused by the…
Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…
We propose a novel method for the efficient and accurate iterative solution of frequency domain integral equations (IEs) that are used for large/multi-scale electromagnetic scattering problems. The proposed method uses a novel…
We consider the numerical approximation of general semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive space-time noise. In contrast to the standard time stepping methods which uses basic increments of…
Boundary integral equations and Nystrom discretization provide a powerful tool for the solution of Laplace and Helmholtz boundary value problems. However, often a weakly-singular kernel arises, in which case specialized quadratures that…
Electroencephalography (EEG) is a neuroimaging technique that records brain neural activity with high temporal resolution. Unlike other methods, EEG does not require prohibitively expensive equipment and can be easily set up using…
This paper develops a high-order selective discontinuous Galerkin (SDG) method for solving elliptic interface problems on interface-unfitted Cartesian meshes. This method applies the discontinuous Galerkin (DG) formulation on interface…
We present superalgebraic compatible Nystr\"om discretizations for the four Helmholtz boundary operators of Calder\'{o}n's calculus on smooth closed curves in 2D. These discretizations are based on appropriate splitting of the kernels…
Harmonic decomposition of surfaces, such as spherical and spheroidal harmonics, is used to analyze morphology, reconstruct, and generate surface inclusions of particulate microstructures. However, obtaining high-quality meshes of…
Compatible schemes localize degrees of freedom according to the physical nature of the underlying fields and operate a clear distinction between topological laws and closure relations. For elliptic problems, the cornerstone in the scheme…
High-order spatial discretisations and full discretisations of parabolic partial differential equations on evolving surfaces are studied. We prove convergence of the high-order evolving surface finite element method, by showing high-order…
High-density electroencephalography (HD-EEG) enables fine-grained measurement of cortical activity but requires expensive hardware and lengthy setup times, limiting its clinical and research accessibility. We propose EMAG (EEG Mixture of…
Boundary integral equation methods are widely used in the solution of many partial differential equations. The kernels that appear in these surface integrals are nearly singular when evaluated near the boundary, and straightforward…
The aim of this work is to apply a semi-implicit (SI) strategy within a Rosenbrock-type and IMEX linear multistep (LM) framework to a sequence of 1D time-dependent partial differential equations (PDEs) with high order spatial derivatives.…
We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together…