Journal ArticleDOI
Rapid solution of integral equations of classical potential theory
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An algorithm is described for rapid solution of classical boundary value problems (Dirichlet an Neumann) for the Laplace equation based on iteratively solving integral equations of potential theory using CPUs proportional to n.About:
This article is published in Journal of Computational Physics.The article was published on 1985-09-15. It has received 1426 citations till now. The article focuses on the topics: Dirichlet problem & Boundary value problem.read more
Citations
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Chemistry with ADF
G. te Velde,F.M. Bickelhaupt,Evert Jan Baerends,C. Fonseca Guerra,S. J. A. van Gisbergen,J.G. Snijders,T. Ziegler +6 more
TL;DR: The “Activation‐strain TS interaction” (ATS) model of chemical reactivity is reviewed as a conceptual framework for understanding how activation barriers of various types of reaction mechanisms arise and how they may be controlled, for example, in organic chemistry or homogeneous catalysis.
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A fast algorithm for particle simulations
TL;DR: An algorithm is presented for the rapid evaluation of the potential and force fields in systems involving large numbers of particles whose interactions are Coulombic or gravitational in nature, making it considerably more practical for large-scale problems encountered in plasma physics, fluid dynamics, molecular dynamics, and celestial mechanics.
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Accelerating t-SNE using tree-based algorithms
TL;DR: Variants of the Barnes-Hut algorithm and of the dual-tree algorithm that approximate the gradient used for learning t-SNE embeddings in O(N log N) are developed and shown to substantially accelerate and make it possible to learnembeddings of data sets with millions of objects.
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A new oniom implementation in gaussian98. part i. the calculation of energies, gradients, vibrational frequencies and electric field derivatives
TL;DR: In this paper, a modified handling of the link atoms which are introduced to terminate the dangling bonds of the model system is presented, which allows the consistent combination of vibrational frequencies and the calculation of other molecular properties such as IR intensities, Raman intensities as well as dipole moments, polarizabilities, and hyperpolarizabilities.
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Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects
TL;DR: Using these techniques, the FMM and MLFMA can solve the problem of electromagnetic scattering by large complex three-dimensional objects such as an aircraft on a small computer.
References
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Book
Introduction to Numerical Analysis
Josef Stoer,Roland Bulirsch +1 more
TL;DR: This well written book is enlarged by the following topics: B-splines and their computation, elimination methods for large sparse systems of linear equations, Lanczos algorithm for eigenvalue problems, implicit shift techniques for theLR and QR algorithm, implicit differential equations, differential algebraic systems, new methods for stiff differential equations and preconditioning techniques.
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Approximate Methods of Higher Analysis
Journal ArticleDOI
Complex Variables and Applications
Book
Complex Variables and Applications
TL;DR: In this paper, Cauchy-Goursat Theorem 2.1.1 was extended to include the point at infinity and the point of infinity at infinity in the definition of differentiability of analytical functions.
Journal ArticleDOI
Calculation of potential flow about arbitrary bodies
J.L. Hess,A.M.O. Smith +1 more
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GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
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