An Approach to the Implementation of Laplace and a Broadband Helmholtz Fast Multipole Method as an Application Independent Library

Authors

  • Sanjay Velamparambil Ansys Inc., 1995 N. 57th Court, Suite 100, Boulder, CO-80301, USA

DOI:

https://doi.org/10.13052/2024.ACES.J.390504

Keywords:

Integral Equations, Fast Multipole Methods

Abstract

In this paper, we propose an approach to develop an application independent library of Laplace and Helmholtz fast multipole method (FMM) that can be used in different applications. For this purpose, we consider a generalized problem and a corresponding canonical problem (defined below). In the first main contribution, we show that it is possible to capture the essential characteristics of the canonical summation from sampling the values of certain potentials or signature functions. In the second main contribution, we show that partial derivatives of arbitrary orders acting on the far field can be represented as product of sparse matrices within the library, transparent to the user. Combining the two ideas, we show that once the FMM is configured to compute the canonical summation, the same setup can be used to work with a much wider, general class of problems.

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Author Biography

Sanjay Velamparambil, Ansys Inc., 1995 N. 57th Court, Suite 100, Boulder, CO-80301, USA

Sanjay Velamparam I obtained a Ph.D. in Engineering from the Indian Institute of Science, Bangalore, in 1997. My doctoral work was in the then nascent field of fast multipole methods (FMM). Subsequently, working with Dr. Weng Chew at the University of Illinois at Urbana-Champaign, I pioneered the parallelization of Helmholtz FMM on distributed memory computers.

I was with Ansoft Corporation (currently Ansys Inc.) from 2002-2005 working on fast integral equation methods for signal integrity applications. In 2007, I joined Acceleware Corporation, Calgary, and worked on linear algebraic algorithms for GPU computing. In 2010, I joined Apache Design Solutions, which was later acquired by Ansys. I have been working on fast integral equation methods for several Ansys products such as Ansys Q3D Extractor® and SIwave™ since 2010.

I enjoy long bicycle rides, especially mountainous routes, running, and generally love the outdoors. I am married and we are fortunate enough to live in the foothills of the majestic Rocky Mountains in Northern Colorado.

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Published

2024-05-31

How to Cite

[1]
S. Velamparambil, “An Approach to the Implementation of Laplace and a Broadband Helmholtz Fast Multipole Method as an Application Independent Library”, ACES Journal, vol. 39, no. 05, pp. 405–415, May 2024.