Results 31 to 40 of about 1,226 (77)

Some Results on the Complexity of Numerical Integration [PDF]

, 2015
This is a survey (21 pages, 124 references) written for the MCQMC 2014 conference in Leuven, April 2014. We start with the seminal paper of Bakhvalov (1959) and end with new results on the curse of dimension and on the complexity of oscillatory integrals.
Novak, Erich
core  

A curved-element unstructured discontinuous Galerkin method on GPUs for the Euler equations

, 2012
In this work we consider Runge-Kutta discontinuous Galerkin methods (RKDG) for the solution of hyperbolic equations enabling high order discretization in space and time. We aim at an efficient implementation of DG for Euler equations on GPUs.
Schmidt, S., Schulz, V., Siebenborn, M.
core   +1 more source

Numerical Integration of Some Arbitrary Functions over an Ellipsoid by Discretizing into Hexahedral Elements for Biomaterial Studies

International Journal of Chemical Engineering, Volume 2024, Issue 1, 2024.
This study mathematically examines chemical and biomaterial models by employing the finite element method. Unshaped biomaterials’ complex structures have been numerically analyzed using Gaussian quadrature rules. It has been analyzed for commercial benefits of chemical engineering and biomaterials as well as biorefinery fields.
T. M. Mamatha, B. Venkatesh, P. Senthil Kumar, S. Mullai Venthan, M. S. Nisha, Gayathri Rangasamy, Jitendra Kumar   +6 more
wiley   +1 more source

A Bayesian Structural Modal Updating Method Based on Sparse Grid and Ensemble Kalman Filter

Structural Control and Health Monitoring, Volume 2024, Issue 1, 2024.
This study presents a sparse grid interpolation and ensemble Kalman filter (EnKF)‐based Markov Chain Monte Carlo (MCMC) method (SG‐EnMCMC). Initiating with the formulation of a recursive equation for the state space vector, derived from the structural dynamic equation, this study adopts a dimensionality reduction strategy.
Guangwei Lin, Yi Zhang, Enjian Cai, Min Luo, Jing Guo, Zili Zhang   +5 more
wiley   +1 more source

Cubature formulas, geometrical designs, reproducing kernels, and Markov operators

, 2005
Cubature formulas and geometrical designs are described in terms of reproducing kernels for Hilbert spaces of functions on the one hand, and Markov operators associated to orthogonal group representations on the other hand.
De La Harpe, Pierre, Pache, Claude
core   +3 more sources

Reconstruction from Radon projections and orthogonal expansion on a ball

, 2007
The relation between Radon transform and orthogonal expansions of a function on the unit ball in $\RR^d$ is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to algorithms for image ...
Bojanov B, Bortfeld T, Caponnetto A, Davison M E, Dunkl C F, Helgason S, Herman G T, Kak A C, Kak A C, Louis A, Maass P, Madych W R, Mysovskikh I P, Natterer F, Stroud A, Szegő G, Yuan Xu, Yuan Xu, Yuan Xu, Yuan Xu Tischenko O   +19 more
core   +1 more source

Fast cubature of high dimensional biharmonic potential based on Approximate Approximations

, 2018
We derive new formulas for the high dimensional biharmonic potential acting on Gaussians or Gaussians times special polynomials. These formulas can be used to construct accurate cubature formulas of an arbitrary high order which are fast and effective ...
Lanzara, Flavia, Maz'ya, Vladimir, Schmidt, Gunther   +2 more
core   +1 more source

Numerical cubature from Archimedes' hat-box theorem

, 2004
Archimedes' hat-box theorem states that uniform measure on a sphere projects to uniform measure on an interval. This fact can be used to derive Simpson's rule.
Kuperberg, Greg
core  

Computation of the magnetostatic interaction between linearly magnetized polyhedrons

, 2016
In this paper we present a method to accurately compute the energy of the magnetostatic interaction between linearly (or uniformly, as a special case) magnetized polyhedrons. The method has applications in finite element micromagnetics, or more generally
Chernyshenko, Dmitri, Fangohr, Hans
core   +1 more source

Note on cubature formulae and designs obtained from group orbits

, 2011
In 1960, Sobolev proved that for a finite reflection group G, a G-invariant cubature formula is of degree t if and only if it is exact for all G-invariant polynomials of degree at most t.
Bajnok, Bajnok, Bannai, Bannai, Bannai, Bannai, Bannai, Delsarte, Delsarte, Erdělyi, Goethals, Hirao, Hiroshi Nozaki, Li, Masanori Sawa, Moody, Mysovskikh, Mysovskikh, Neumaier, Nozaki, Sali, Salikhov, Sobolev, Stroud, Verlinden, Xu   +25 more
core   +1 more source