Related papers: VMS spectral solution of two-dimensional advection…
A novel method to improve the accuracy of pressure field estimation from time-resolved Particle Image Velocimetry data is proposed. This method generates several new time-series of velocity field by propagating in time the original one…
The present paper introduces an efficient and accurate numerical scheme for the solution of a highly anisotropic elliptic equation, the anisotropy direction being given by a variable vector field. This scheme is based on an asymptotic…
An adjoint-based variational optimal mixed model (VOMM) is proposed for subgrid-scale (SGS) closure in large-eddy simulation (LES) of turbulence. The stabilized adjoint LES equations are formulated by introducing a minimal regularization to…
In this paper, we analyze two classes of spectral volume (SV) methods for one-dimensional hyperbolic equations with degenerate variable coefficients. The two classes of SV methods are constructed by letting a piecewise $k$-th order ($k\ge…
In this work, we develop a Legendre spectral element method (LSEM) for solving the stochastic nonlinear system of advection-reaction-diffusion models. The used basis functions are based on a class of Legendre functions such that their mass…
We consider the applications of a numerical-analytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of Vlasov-Poisson/Maxwell equations. We calculate the…
A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…
We propose a general class of five-dimensional soft-wall models with AdS metric near the ultraviolet brane and four-dimensional Poincar\'e invariance, where the infrared scale is determined dynamically. A large UV/IR hierarchy can be…
We present a robust and accurate numerical method for the anisotropic diffusion equation in curvilinear coordinates. This study extends the recent work [Muir et al., Computer Physics Communications, 2025] for solving the anisotropic…
A novel approach for the stabilization of the Spectral-Volume (SV) method based on Dafermos' entropy rate criterion is presented. The method is an adaption of an already existing approach for the stabilization of the Discontinuous-Galerkin…
This paper addresses the topological structure of steady, anisotropic, inhomogeneous diffusion problems. Two discrete formulations: a) mixed and b) direct formulations are discussed. Differential operators are represented by sparse…
We present the variational multiscale (VMS) method for partial differential equations (PDEs) with stochastic coefficients and source terms. We use it as a method for generating accurate coarse-scale solutions while accounting for the effect…
We develop a novel and efficient iterative scheme for solving incompressible steady Navier-Stokes equations. The method is an adaptation of the Incremental Viscosity Splitting approximation for unsteady flows to steady equations. At each…
We consider frequency-weighted damping optimization for vibrating systems described by a second-order differential equation. The goal is to determine viscosity values such that eigenvalues are kept away from certain undesirable areas on the…
A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid…
In this paper, we propose a novel unstructured mesh control volume method to deal with the space fractional derivative on arbitrarily shaped convex domains, which to the best of our knowledge is a new contribution to the literature.…
We consider distributed multitask learning problems over a network of agents where each agent is interested in estimating its own parameter vector, also called task, and where the tasks at neighboring agents are related according to a set…
This work focuses on numerically solving a shape identification problem related to advection-diffusion processes with space-dependent coefficients using shape optimization techniques. Two boundary-type cost functionals are considered, and…
We introduce a proximal version of the stochastic dual coordinate ascent method and show how to accelerate the method using an inner-outer iteration procedure. We analyze the runtime of the framework and obtain rates that improve…
A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and…