Related papers: A fast Fourier spectral method for the linearized …
At higher altitudes, for high temperature gases, for instance near space shuttles moving at hypersonic speed, not only mechanical collisions are affecting the gas flow, but also chemical reactions have an impact on such hypersonic flows. In…
We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix in a recursive manner, we embed an approximation of the…
We present a spectrally accurate fast algorithm for evaluating the solution to the scalar wave equation in free space driven by a large collection of point sources in a bounded domain. With $M$ sources temporally discretized by $N_t$ time…
This work explores the capability of simulating complex fluid flows by directly solving the Boltzmann equation. Due to the high-dimensionality of the governing equation, the substantial computational cost of solving the Boltzmann equation…
The paper presents a solution to the Boltzmann kinetic equation based on the construction of its discrete conservative model. Discrete analogue of the collision integral is presented as a contraction of a tensor, which is independent from…
In this paper we present a new ultra efficient numerical method for solving kinetic equations. In this preliminary work, we present the scheme in the case of the BGK relaxation operator. The scheme, being based on a splitting technique…
A variational approach is used to develop a robust numerical procedure for solving the nonlinear Poisson-Boltzmann equation. Following Maggs et al., we construct an appropriate constrained free energy functional, such that its…
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…
I describe a Lanczos method to compute the Neuberger Operator and a multigrid algorithm for its inversion.
Quantum algorithms offer an exponential advantage with respect to the number of dependent variables for solving certain nonlinear ordinary differential equations (ODEs). These algorithms typically begin by transforming the original…
We present efficient algorithms for computing the $N$-point correlation functions (NPCFs) of random fields in arbitrary $D$-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences, and provide a…
We developed fast direct solver for 3D Helmholtz and Maxwell equations in layered medium. The algorithm is based on the ideas of cyclic reduction for separable matrices. For the grids with major uniform part (within the survey domain in the…
In computational molecular science, calculation of electrostatic interactions involving charged atoms - the strongest interactions in condensed phases, is a major bottleneck. We propose a quantum-classical algorithm for fast, yet, accurate…
This paper presents a novel Fourier spectral method that utilizes optimization techniques to ensure the positivity and conservation of moments in the space of trigonometric polynomials. We rigorously analyze the accuracy of the new method…
We present the first numerical implementation of a non-perturbative renormalization method for lattice operators, based on the study of correlation functions in coordinate space at short Euclidean distance. The method is applied to compute…
We introduce a structured approach to the construction of linear BGK-type collision operators ensuring that the resulting Lattice-Boltzmann methods are stable with respect to a weighted $L^2$-norm. The results hold for particular boundary…
We consider the neural sparse representation to solve Boltzmann equation with BGK and quadratic collision model, where a network-based ansatz that can approximate the distribution function with extremely high efficiency is proposed.…
Scalar diffraction calculations such as the angular spectrum method (ASM) and Fresnel diffraction, are widely used in the research fields of optics, X-rays, electron beams, and ultrasonics. It is possible to accelerate the calculation using…
The paper describes a numerical method for solving acoustic multibody scattering problems in two and three dimensions. The idea is to compute a highly accurate approximation to the scattering operator for each body through a local…
We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle…