Search results for "fast gauss transform"
showing 4 items of 4 documents
Towards an Efficient Implementation of an Accurate SPH Method
2020
A modified version of the Smoothed Particle Hydrodynamics (SPH) method is considered in order to overcome the loss of accuracy of the standard formulation. The summation of Gaussian kernel functions is employed, using the Improved Fast Gauss Transform (IFGT) to reduce the computational cost, while tuning the desired accuracy in the SPH method. This technique, coupled with an algorithmic design for exploiting the performance of Graphics Processing Units (GPUs), makes the method promising, as shown by numerical experiments.
Improved fast Gauss transform for meshfree electromagnetic transients simulations
2019
Abstract In this paper improved fast summations are introduced to enhance a meshfree solver for the evolution of the electromagnetic fields over time. The original method discretizes the time-domain Maxwell’s curl equations via Smoothed Particle Hydrodynamics requiring many summations on the first derivatives of the kernel function and field vectors at each time step. The improved fast Gauss transform is properly adopted picking up the computational cost and the memory requirement at an acceptable level preserving the accuracy of the computation. Numerical simulations in two-dimensional domains are discussed giving evidence of improvements in the computation compared to the standard formula…
Path integral solution handled by Fast Gauss Transform
2009
Abstract The path integral solution method is an effective tool for evaluating the response of non-linear systems under Normal White Noise, in terms of probability density function (PDF). In this paper it has been observed that, using short-time Gaussian approximation, the PDF at a given time instant is the Gauss Transform of the PDF at an earlier close time instant. Taking full advantage of the so-called Fast Gauss Transform a new integration method is proposed. In order to overcome some unsatisfactory trends of the classical Fast Gauss Transform, a new version termed as Symmetric Fast Gauss Transform is also proposed. Moreover, extensions to the two Fast Gauss Transform to MDOF systems ar…
A CUDA-based implementation of an improved SPH method on GPU
2021
We present a CUDA-based parallel implementation on GPU architecture of a modified version of the Smoothed Particle Hydrodynamics (SPH) method. This modified formulation exploits a strategy based on the Taylor series expansion, which simultaneously improves the approximation of a function and its derivatives with respect to the standard formulation. The improvement in accuracy comes at the cost of an additional computational effort. The computational demand becomes increasingly crucial as problem size increases but can be addressed by employing fast summations in a parallel computational scheme. The experimental analysis showed that our parallel implementation significantly reduces the runti…