Related papers: Fast algorithms for computing the Boltzmann collis…
In this work the algorithms of fast multiplication of matrices are considered. To any algorithm there associated a certain group of automorphisms. These automorphism groups are found for some well-known algorithms, including algorithms of…
In recent years, quantum Boltzmann methods have gained more and more interest as they might provide a viable path towards solving fluid dynamics problems on quantum computers once this emerging compute technology has matured and…
We develop a machine learning method to construct accurate ground-state wave functions of strongly interacting and entangled quantum spin as well as fermionic models on lattices. A restricted Boltzmann machine algorithm in the form of an…
Petaflop architectures are currently being utilized efficiently to perform large scale computations in Atomic, Molecular and Optical Collisions. We solve the Schroedinger or Dirac equation for the appropriate collision problem using the…
We discuss two topics that we have encountered in our lattice-Boltzmann simulations of complex fluids: the sizes of droplets in particle-stabilised emulsions and deformable particles in fluid flow. The common factor in these seemingly…
The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved…
The linearized collision operator of the Boltzmann equation can in a natural way be written as a sum of a positive multiplication operator, the collision frequency, and an integral operator. Compactness of the integral operator for…
This study addresses the challenge of simulating realistic particle systems by proposing a novel particle decomposition scheme that improves the parallel performance of surface resolved particle simulations. Realistic particle systems often…
An efficient numerical algorithm is presented for massively parallel simulations of dispersion-managed wavelength-division-multiplexed optical fiber systems. The algorithm is based on a weak nonlinearity approximation and independent…
The numerical simulation of multiphase flows involving dispersed components with large scale disparities, such as the collisions between millimeter-sized bubbles and micron-sized mineral particles in flotation, poses a significant…
Despite rapid progress in the development of quantum algorithms in quantum computing as well as numerical simulation methods in classical computing for atomic and molecular applications, no systematic and comprehensive electronic structure…
High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…
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…
Particle interactions are key elements of many dynamical systems. In the context of systems described by a Boltzmann equation, such interactions may be described by a collision integral, a multidimensional integral over the momentum-phase…
This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…
We attempt the use of a unitary operator to approximate the lattice Boltzmann collision operator. We use a modified amplitude encoding to bypass the renormalization that would have required classical processing at every step (thus eroding…
While fast multipole methods (FMMs) are in widespread use for the rapid evaluation of potential fields governed by the Laplace, Helmholtz, Maxwell or Stokes equations, their coupling to high-order quadratures for evaluating layer potentials…
Particle collisions are the primary mechanism of inter-particle momentum and energy exchange for dense particle-laden flow. Accurate approximation of this collision operator in four-way coupled Euler-Lagrange approaches remains challenging…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
We propose an entropic Fourier method for the numerical discretization of the Boltzmann collision operator. The method, which is obtained by modifying a Fourier Galerkin method to match the form of the discrete velocity method, can be…