Related papers: A New High-Performing Method for Solving the Homog…
The computational homogenization of hyperelastic solids in the geometrically nonlinear context has yet to be treated with sufficient efficiency in order to allow for real-world applications in true multiscale settings. This problem is…
Techniques like speckle holography and shearography are rarely applied due to the complexity of instrument setup and lack of automated result analysis, despite their potential. By simulating speckle interferometric outcomes, we seek to…
A finite element approach to solve numerically the Takagi-Taupin equations expressed in a weak form is presented and applied to simulate X-ray reflectivity curves, spatial intensity distributions and focusing properties of bent perfect…
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…
Full-waveform inversion (FWI) is an effective method for imaging subsurface properties using sparsely recorded data. It involves solving a wave propagation problem to estimate model parameters that accurately reproduce the data. Recent…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…
Boundary element methods for the Helmholtz equation lead to large dense matrices that can only be handled if efficient compression techniques are used. Directional compression techniques can reach good compression rates even for…
The paper deals with optimization of the acoustic band gaps computed using the homogenized model of strongly heterogeneous elastic composite which is constituted by soft inclusions periodically distributed in stiff elastic matrix. We employ…
We present the Wavelet-based Edge Multiscale Parareal (WEMP) Algorithm, recently proposed in [Li and Hu, {\it J. Comput. Phys.}, 2021], for efficiently solving subdiffusion equations with heterogeneous coefficients in long time. This…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
Seismic imaging is a major challenge in geophysics with broad applications. It involves solving wave propagation equations with absorbing boundary conditions (ABC) multiple times. This drives the need for accurate and efficient numerical…
The surrogate matrix methodology delivers low-cost approximations of matrices (i.e., surrogate matrices) which are normally computed in Galerkin methods via element-scale quadrature formulas. In this paper, the methodology is applied to a…
In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for…
Modeling extreme-mass-ratio inspirals hinges on the accurate and efficient computation of gravitational-wave fluxes from generic Kerr orbits. Conventional frequency-domain techniques are often limited by costly auxiliary parameter searches…
Two accelerated imaginary-time evolution methods are proposed for the computation of solitary waves in arbitrary spatial dimensions. For the first method (with traditional power normalization), the convergence conditions as well as…
We propose an iterative solution method for the 3D high-frequency Helmholtz equation that exploits a contour integral formulation of spectral projectors. In this framework, the solution in certain invariant subspaces is approximated by…
This work presents a Boundary Element Method (BEM) formulation for contactless electromagnetic field assessments. The new scheme is based on a regularized BEM approach that requires the use of electric measurements only. The regularization…
Variational-hemivariational inequalities are an important mathematical framework for nonsmooth problems. The framework can be used to study application problems from physical sciences and engineering that involve non-smooth and even…
The heat equation is often used in order to inpaint dropped data in inpainting-based lossy compression schemes. We propose an alternative way to numerically solve the heat equation by an extended Krylov subspace method. The method is very…
We introduce a new method for studying stochastic homogenization of elliptic equations in nondivergence form. The main application is an algebraic error estimate, asserting that deviations from the homogenized limit are at most proportional…