Related papers: Wavelet-Fourier CORSING techniques for multi-dimen…
The proper orthogonal decomposition (POD) is a powerful classical tool in fluid mechanics used, for instance, for model reduction and extraction of coherent flow features. However, its applicability to high-resolution data, as produced by…
The numerical approximation of some Boussinesq systems in two spatial dimensions is here considered. The differential systems under study are proposed as asymptotic models for the propagation of waves along the interface of two layers of…
A computational technique has been developed to perform compressible flow simulations involving moving boundaries using an embedded boundary approach within the block-structured adaptive mesh refinement framework of AMReX. A conservative,…
Physics-guided sampling with diffusion priors has recently shown strong performance in solving complex systems of partial differential equations (PDEs) from sparse observations. However, these methods are typically evaluated on benchmark…
This paper proposes to address the issue of complexity reduction for the numerical simulation of multiscale media in a quasi-periodic setting. We consider a stationary elliptic diffusion equation defined on a domain $D$ such that…
In this paper we study elliptic partial differential equations with rapidly varying diffusion coefficient that can be represented as a perturbation of a reference coefficient. We develop a numerical method for efficiently solving multiple…
We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…
Recently it has been established that asymptotic incoherence can be used to facilitate subsampling, in order to optimize reconstruction quality, in a variety of continuous compressed sensing problems, and the coherence structure of certain…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the third paper, the analytical analysis of multiscale phenomena inherent in the…
Optical tomographic reconstruction of a 3D nanoscale specimen is hindered by the axial diffraction limit, which is 2-3 times worse than the focal plane resolution. We propose and experimentally demonstrate an axial super-resolution…
Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…
This paper presents the development and analysis of a streamline upwind/Petrov-Galerkin (SUPG) method for the magnetic advection-diffusion problem. A key feature of the method is an SUPG-type stabilization term based on the residuals and…
In this paper the projection hybrid FV/FE method presented in Busto et al. 2014 is extended to account for species transport equations. Furthermore, turbulent regimes are also considered thanks to the $k-\varepsilon$ model. Regarding the…
We study the problem of multi-compression and reconstructing a stochastic signal observed by several independent sensors (or compressors) that transmit compressed information to a fusion center. { The key aspect of this problem is to find…
High-fidelity, high-resolution numerical simulations are crucial for studying complex multiscale phenomena in fluid dynamics, such as turbulent flows and ocean waves. However, direct numerical simulations with high-resolution solvers are…
Methods to solve the relativistic hydrodynamic equations are a key computational kernel in a large number of astrophysics simulations and are crucial to understanding the electromagnetic signals that originate from the merger of…
In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence…
This paper is concerned with the convergence of a series associated with a certain version of the convexification method. That version has been recently developed by the research group of the first author for solving coefficient inverse…
In this paper, we aim to study the diffusion approximation for multi-scale McKean-Vlasov stochastic differential equations. More precisely, we prove the weak convergence of slow process $X^\varepsilon$ in $C([0,T];\mathbb{R}^n)$ towards the…
We present the applications of variational-wavelet approach for computing multiresolution/multiscale representation for solution of some approximations of Vlasov-Maxwell-Poisson equations.