202,476 research outputs found
Some Results on the Complexity of Numerical Integration
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. Some small errors of earlier versions are corrected
Modernizing PHCpack through phcpy
PHCpack is a large software package for solving systems of polynomial
equations. The executable phc is menu driven and file oriented. This paper
describes the development of phcpy, a Python interface to PHCpack. Instead of
navigating through menus, users of phcpy solve systems in the Python shell or
via scripts. Persistent objects replace intermediate files.Comment: Part of the Proceedings of the 6th European Conference on Python in
Science (EuroSciPy 2013), Pierre de Buyl and Nelle Varoquaux editors, (2014
An Unsplit Godunov Method for Ideal MHD via Constrained Transport in Three Dimensions
We present a single step, second-order accurate Godunov scheme for ideal MHD
which is an extension of the method described by Gardiner & Stone (2005) to
three dimensions. This algorithm combines the corner transport upwind (CTU)
method of Colella for multidimensional integration, and the constrained
transport (CT) algorithm for preserving the divergence-free constraint on the
magnetic field. We describe the calculation of the PPM interface states for 3D
ideal MHD which must include multidimensional ``MHD source terms'' and
naturally respect the balance implicit in these terms by the condition. We compare two different forms for the CTU integration
algorithm which require either 6- or 12-solutions of the Riemann problem per
cell per time-step, and present a detailed description of the 6-solve
algorithm. Finally, we present solutions for test problems to demonstrate the
accuracy and robustness of the algorithm.Comment: Extended version of the paper accepted for publication in JC
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