1,721,062 research outputs found
Enhancing the iterative smoothed particle hydrodynamics method
Full text linkMotivated by recent research on the iterative approach proposed for the smoothed particle hydrodynamics (ISPH) method, some ideas to improve the process are introduced. The standard procedure is enhanced iterating on the residuals preserving the matrix-free nature of the process. The method is appealing providing reasonable results with disordered data distribution too and no kernel variations are needed in the approximation. This work moves forward with a novel formulation requiring a lower number of iterations to reach a desired accuracy. The computational procedure is described and some results are introduced to appreciate the proposed formulation
The enriched multinode Shepard collocation method for solving elliptic problems with singularities
Full text linkIn this paper, the multinode Shepard method is adopted for the first time to numerically solve a differential problem with a discontinuity in the boundary. Starting from previous studies on elliptic boundary value problems, here the Shepard method is employed to catch the singularity on the boundary. Enrichments of the functional space spanned by the multinode cardinal Shepard basis functions are proposed to overcome the difficulties encountered. The Motz's problem is considered as numerical benchmark to assess the method. Numerical results are presented to show the effectiveness of the proposed approach
Improved fast Gauss transform for meshfree electromagnetic transients simulations
Full text linkIn 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 formulation
Electric scalar potential estimations for non-invasive brain activity detection through multinode Shepard method
No full textElectric scalar potential estimation is a key step for non-invasive investigations of brain activity with high time resolutions. The neural sources can be reconstructed by solving a typical inverse problem based on a forward problem formulated as a set of boundary value problems coupled by interface conditions. In this paper, we propose a Shepard multinode method to numerically estimate electric scalar potentials via collocation. The method is based on a special kind of inverse distance weighting partition of unity method to increase polynomial precision, approximation order, and accuracy of the classical Shepard approximation. The barycentric form, through the use of cardinal basis function, is adopted to generate Shepard interpolants with high polynomial reproduction order. Comparisons with the analytic solution and the standard Shepard method are provided to assess the proposed approach
Polynomial mapped bases: theory and applications
Full text linkIn this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-imaging reconstruction. The method relies on polynomial mapped bases allowing, for instance, to incorporate data or function discontinuities in a suitable mapping function. The new technique substantially mitigates the Runge's and Gibbs effects
An adaptive algorithm for determining the optimal degree of regression in constrained mock-Chebyshev least squares quadrature
Full text linkIn this paper we develop an adaptive algorithm for determining the optimal degree of regression in the constrained mock-Chebyshev least-squares interpolation of an analytic function to obtain quadrature formulas with high degree of exactness and accuracy from equispaced nodes. We numerically prove the effectiveness of the proposed algorithm by several examples
A CUDA-based implementation of an improved SPH method on GPU
Full text linkWe 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 runtime, with speed-ups of up to 90,when compared to the CPU-based implementation
Regularization of optical flow with M-band wavelet transform
No full textThe optical flow is an important tool for problems arising in the analysis of image sequences. Flow fields generated by various existing solving techniques are often noisy and partially incorrect, especially near occlusions or motion boundaries. Therefore, the additional information on the scene gained from a sequence of images is usually worse. In this paper, discrete wavelet transform has been adopted in order to enhance the reliability of optical flow estimation. A generalization of the well-known dyadic orthonormal wavelets to the case of the dilation scale factor M > 2 with N vanishing moments has been used, and it has proved to be a useful regularizing tool. The advantages in the computations have been shown by experimental results performed on real image sequences. © 2003 Elsevier Science Ltd. All rights reserved
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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