The continuum theory applied to bimolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and […]

September 17, 2013 by hgpu

The lattice Boltzmann equation (LBE) method is a promising technique for simulating fluid flows and modeling complex physics. Because the LBE model is based on microscopic models and mesoscopic kinetic equations, it offers many advantages for the study of multi-component or multiphase flows. However, there are still challenges encountered when dealing with thermal effects and […]

May 15, 2013 by hgpu

The PyGBe code solves the linearized Poisson-Boltzmann equation using a boundary-integral formulation. We use a boundary element method with a collocation approach, and solve it via a Krylov-subspace method. To do this efficiently, the matrix-vector multiplications in the Krylov iterations are accelerated with a treecode, achieving O(N log N) complexity. The code presents a Python […]

January 31, 2013 by hgpu

With the advent of low-energy buildings, the need for accurate building performance simulations has significantly increased. However, for the time being, the thermo-aeraulic effects are often taken into account through simplified or even empirical models, which fail to provide the expected accuracy. Resorting to computational fluid dynamics seems therefore unavoidable, but the required computational effort […]

January 24, 2013 by hgpu

Lattice group models (LGpM) are kinetic models on integer lattices derived from the automorphism group of the lattice. In the last decades it was too expensive to simulate large systems (100 – 1000 velocities in a 2D or 3D model), with complex physical two or three dimensional domains, on normal computers or clusters within an […]

October 14, 2012 by hgpu

We show how to accelerate the direct solution of the Boltzmann equation using Graphics Processing Units (GPUs). In order to fully exploit the computational power of the GPU, we choose a method of solution which combines a finite difference discretization of the free-streaming term with a Monte Carlo evaluation of the collision integral. The efficiency […]

January 18, 2012 by hgpu

We show how to accelerate the numerical solution of the Boltzmann equation for a binary gas mixture by using Graphics Processing Units (GPUs). In order to fully exploit the computational power of the GPU, we adopt a semi-regular method of solution which combines a finite difference discretization of the free-streaming term with a Monte Carlo […]

January 8, 2012 by hgpu

While the Monte Carlo method for the Boltzmann transport equation for semiconductors has already been parallelized, this is much more difficult to accomplish for the deterministic spherical harmonics expansion method which requires the solution of a linear system of equations. For the typically employed iterative solvers, preconditioners are required to obtain good convergence rates. These […]

November 29, 2011 by hgpu

The paper describes specific features of parallelization of collision integral computation algorithms, which are conditioned by the CUDA architecture of parallelization on graphic cards [1].

November 6, 2011 by hgpu

GPU-accelerated computing of the Boltzmann collision integral is studied using deterministic method with piecewise approximation of the velocity distribution function and analytical integration over collision impact parameters. The acceleration of 40 times is achieved compared to CPU calculations for a 3D problem of collisional relaxation of bi-Maxwellian velocity distribution.

November 5, 2011 by hgpu

The solution of large systems of linear equations is typically achieved by iterative methods. The rate of convergence of these methods can be substantially improved by the use of preconditioners, which can be either applied in a black-box fashion to the linear system, or exploit properties specific to the underlying problem for maximum efficiency. However, […]

October 10, 2011 by hgpu

Design of data structures for high performance computing (HPC) is one of the principal challenges facing researchers looking to utilize heterogeneous computing machinery. Heterogeneous systems derive cost, power, and speed efficiency by being composed of the appropriate hardware for the task. Yet, each type of processor requires a specific organization of the application state in […]

October 6, 2011 by hgpu