Comparison of Clenshaw-Curtis and Leja Quasi-Optimal Sparse Grids for the Approximation of Random PDEs

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The method of moments (MOM), as introduced by R. F. Harrington more than 50 years ago, is reviewed in the context of the classic potential integral equation (PIE) formulations applied to both electrostatic (part 1) and electrodynamic, or full-wave, problem ...

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In this work, we propose a numerical approach based on forward coupled mode modeling to simultaneously evaluate second- and third-order nonlinearities inside a dispersion-engineered waveguide towards the goal of generating broadband terahertz (THz) radiati ...

The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of empirical means of de ...

Compressive tests on clay tiles used in historical masonry timbrel vaults are hindered by the relatively small thickness of the specimens, resulting in buckling or confinement problems depending on the loading direction. This paper presents an experimental ...

We introduce a new numerical method for the time-dependent Maxwell equations on unstructured meshes in two space dimensions. This relies on the introduction of a new mesh, which is the barycentric-dual cellular complex of the starting simplicial mesh, and ...

Mathematical models involving multiple scales are essential for the description of physical systems. In particular, these models are important for the simulation of time-dependent phenomena, such as the heat flow, where the Laplacian contains mixed and ind ...

A new numerical method based on numerical homogenization and model order reduction is introduced for the solution of multiscale inverse problems. We consider a class of elliptic problems with highly oscillatory tensors that varies on a microscopic scale. W ...

We consider an adaptive isogeometric method (AIGM) based on (truncated) hierarchical B-splines and present the study of its numerical properties. By following [10, 12, 11], optimal convergence rates of the AIGM can be proved when suitable approximation cla ...

The Finite Volume Particle Method (FVPM) is a meshless method for simulating fluid flows which includes many of the desirable features of mesh-based finite volume methods. FVPM benefits from particle interaction vectors to weight conservative fluxes exchan ...

In this work we provide a convergence analysis for the quasi-optimal version of the sparse-grids stochastic collocation method we presented in a previous work: “On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods” ...

In focusing Kerr media, small- scale filamentation is the major obstacle to imaging at high light intensities. In this article, we experimentally and numerically demonstrate a method based on statistical averaging to reduce the detrimental effects of filam ...

Dynamic crack branching instabilities in a brittle material are studied numerically by using a non-local damage model. PMMA is taken as our model brittle material. The simulated crack patterns, crack velocities and dissipated energies, compare favorably to ...

We consider the numerical simulation of integrated heart models for the study of the cardiac functioning with particular emphasis on the coupling of the muscle contraction, the fluid dynamics of the left ventricle, and the interaction with the valves. We a ...

An efficient and accurate method, based on the weighted averages (WA) extrapolation technique, is presented for the evaluation of semi-infinite range integrals involving products of Bessel functions of arbitrary order. The method requires splitting the int ...

The direct evaluation method tailored to the 4-D singular integrals over vertex adjacent triangles, arising in the first-kind and second-kind Fredholm surface integral equation formulations, is presented. A combination of singularity cancellation, reorderi ...

Surface Mixed Potential Integral Equation (MPIE) formulations together with the Method of Moments (MoM) are widely used to solve electromagnetic problems. An accurate evaluation of the Green functions (GF) associated to the integral equation and of the cou ...

Large-eddy simulation (LES) of atmospheric boundary layer (ABL) flow is performed over a homogeneous surface with different heat flux forcings. The goal is to test the performance of dynamic subgrid-scale models in a numerical framework and to compare the ...

Comparison of Clenshaw-Curtis and Leja Quasi-Optimal Sparse Grids for the Approximation of Random PDEs

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Roger F. Harrington and the Method of Moments: Part 1: Electrostatics

Low-Rank Tensor Methods for High-Dimensional Problems

Ultra-broadband terahertz radiation by supercontinuum generation and optical rectification in a dispersion-engineered waveguide: a numerical study

Tensor approximation of the self-diffusion matrix of tagged particle processes

Experimental setup and numerical evaluation of the compression test on thin tiles for masonry timbrel vaults

An arbitrary-order Cell Method with block-diagonal mass-matrices for the time-dependent 2D Maxwell equations

Numerical methods for deterministic and stochastic differential equations with multiple scales and high contrasts

Numerical Homogenization And Model Order Reduction For Multiscale Inverse Problems

Adaptive Isogeometric Methods With Hierarchical Splines: An Overview

Development of a finite volume particle method for 3-D fluid flow simulations

Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs

Improving the quality of filament-impaired images in Kerr media by statistical averaging

A non-local continuum damage approach to model dynamic crack branching

Coupled models for integrated heart simulations: a numerical study of the fluid dynamics in the left ventricle

The weighted averages method for semi-infinite range integrals involving products of Bessel functions

On the direct evaluation of surface integral equation impedance matrix elements involving point singularities

Contribution to Integral Equation Techniques for Solving Electromagnetic Problems

Numerical study of dynamic Smagorinsky models in large-eddy simulation of the atmospheric boundary layer: Validation in stable and unstable conditions