Related papers: Finite difference numerical method for the superla…

We present an algorithm for solving the one-dimensional space collisional Boltzmann transport equation (BTE) for electrons in low-temperature plasmas (LTPs). Modeling LTPs is useful in many applications, including advanced manufacturing,…

The late-time dynamics of quantum many-body systems is organized in distinct dynamical universality classes, characterized by their conservation laws and thus by their emergent hydrodynamic transport. Here, we study transport in the…

The mechanism driving core-collapse supernovae is sensitive to the interplay between matter and neutrino radiation. However, neutrino radiation transport is very difficult to simulate, and several radiation transport methods of varying…

Lattice spin models are useful for studying critical phenomena and allow the extraction of equilibrium and dynamical properties. Simulations of such systems are usually based on Monte Carlo (MC) techniques, and the main difficulty is often…

We present a numerical method for the velocity-space, spatially homogeneous, collisional Boltzmann equation for electron transport in low-temperature plasma (LTP) conditions. Modeling LTP plasmas is useful in many applications, including…

We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…

In this thesis we develop techniques to efficiently solve numerical Partial Differential Equations (PDEs) using Graphical Processing Units (GPUs). Focus is put on both performance and re--usability of the methods developed, to this end a…

We present a novel framework for the development of fourth-order lattice Boltzmann schemes to tackle multidimensional nonlinear systems of conservation laws. As for other numerical schemes for hyperbolic problems, high-order accuracy…

We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…

In this article two implementations of a symmetric finite difference algorithm for a first-order partial differential equation are discussed. The considered partial differential equation discribes the time evolution of the crack length…

We present a novel, hardware-agnostic implementation strategy for lattice Boltzmann (LB) simulations, which yields massive performance on homogeneous and heterogeneous many-core platforms. Based solely on C++17 Parallel Algorithms, our…

Solving the three-dimensional (3D) Bratu equation is highly challenging due to the presence of multiple and sharp solutions. Research on this equation began in the late 1990s, but there are no satisfactory results to date. To address this…

This paper introduces JAX-BTE, a GPU-accelerated, differentiable solver for the phonon Boltzmann Transport Equation (BTE) based on differentiable programming. JAX-BTE enables accurate, efficient and differentiable multiscale thermal…

We investigate two-fluid BGK kinetic methods for binary fluids. The developed theory works for asymmetric as well as symmetric systems. For symmetric systems it recovers Sirovich's theory and is summarized in models A and B. For asymmetric…

GPUs offer several times the floating point performance and memory bandwidth of current standard two socket CPU servers, e.g. NVIDIA C2070 vs. Intel Xeon Westmere X5650. The lattice Boltzmann method has been established as a flow solver in…

The lattice Boltzmann method exhibits excellent scalability on current supercomputing systems and has thus increasingly become an alternative method for large-scale non-stationary flow simulations, reaching up to a trillion grid nodes.…

A set of equations is derived from the Boltzmann kinetic equation describing charge transport in semiconductors. The unknowns of these equations depend on the space-time coordinates and the electron energy. The non-parabolic and parabolic…

Numerical simulation results of basic exactly solvable fluid flows using the previously proposed Lattice Boltzmann Method (LBM) formulated on a general curvilinear coordinate system are presented. As was noted in the theoretical work of H.…

The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…

We describe initial work on an extension of the Kaldi toolkit that supports weighted finite-state transducer (WFST) decoding on Graphics Processing Units (GPUs). We implement token recombination as an atomic GPU operation in order to fully…