Fast Multipole Methods: Fundamentals and Applications

 

Instructors: Ramani Duraiswami  & Nail A. Gumerov

Course No. CMSC 878R/AMSC 698R

Note: non CS students must register for the course as AMSC 698R

 

http://www.umiacs.umd.edu/~ramani/cmsc878R/outline.html

E-mail: ramani@umiacs.umd.edu; gumerov@umiacs.umd.edu

class email: cmsc878r AT umiacs.umd.edu

 

Fall 2003, Tuesdays and Thursdays, 3:30 p.m. 4:45 p.m.,

Location: CSI 2118

 

Homework is given on Thursdays at the end of the class and due on the next
Tuesday at the beginning of class

 

Course Outline

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Lecture Notes

(Some of the material here is now also described in the book  Fast Multipole Methods for the Helmholtz Equation in Three Dimensions (The Elsevier Electromagnetism Series))

DATE

LECTURE

CONTENTS

09/02/2003

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Lecture 1

Introduction, Course rules, exams

Applications: Physics, Computer Vision, etc.

Simple example of factorization for degenerate kernel

Asymptotic Complexity. Examples of complexity

Review of Publications.

09/04/2003

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Lecture 2

Review of the factorization idea

Structured Matrices

Integral Equations

Fast Fourier Transform

Homework 1
Solution

Scribe Notes

Simple factorization example.

Intro to Matlab.

09/09/2003

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Lecture 3

Factorization

Regular and Singular Expansions. Taylor Series,

Error Analysis.

09/11/2003

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Lecture 4 Series expansions for factorization
Kronecker products
Compression of series
Homework 2 Solution Fast Gauss transform based on Taylor Series
09/16/2003
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Lecture 5 Near/Far Singular/Regular Expansions
Example of S and R expansions of a singular function
Error bounds
09/18/2003 Lecture 6 Class canceled due to Hurricane Isabel
09/23/2003
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Lecture 6 Splitting of the FMM sum
Spatial ordering
The Pre-FMM algortithm using R expansions and S expansions
Optimization of the number of boxes in the Pre-FMM
Complexity of the Pre-FMM
09/25/2003
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Lecture 7 Introduction to translation operators
Homework 3/4 Solution Implementation of Data Structures for 1-D Pre-FMM
09/30/2003
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Lecture 8 (based on notes of previous lecture)
10/02/2003
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Lecture 9 Single Level FMM (SLFMM)
10/07/2003
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Lecture 10 Review
10/09/2003
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Lecture 11 Multilevel FMM
Homework 5 Solution S, R and S|R translation in one dimension. Error bounds
10/14/2003
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Lecture 12 Hierarchical Data Structures for space sub-division
10/16/2003
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Lecture 13 Hierarchical Data Structures for space sub-division
Homework 6 Solution
10/21/2003
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Lecture 14 Bit interleaving and deinterleaving
10/23/2003 Mid Term Exam Solution
Homework 7 Solution Data Structures
10/28/03
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Lecture 15 Introduction to iterative methods for use with the FMM
10/30/03
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Lecture 16 Review of Exam and previous class
Complexity of MLFMM
Homework 8 1-D MLFMM
11/02/03
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Lecture 17 Review of MLFMM
Error analysis of the MLFMM-I
Project Info.
11/04/03
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Lecture 18 Error analysis of the MLFMM-II
 
Homework 9 Project Preliminary report (See Lecture 17)
11/11/03
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Lecture 19 FMM for the Gravitational/Coulombic potential. Introduction to Spherical Harmonics.
11/13/03 Lecture 20* Guest Lecture by Zhihui Tang: Fast translation operators for the Laplace equation in 2-D and 3-D based on structured matrix decompositions
Homework 10 Project Report: S, R, S|S, S|R , R|R operator evaluation
11/18/03 Lecture 21* General theory of diagonal forms for the FMM
11/20/03
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Lecture 22 Theory of the adaptive FMM
11/25/03
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Lecture 23 Adaptive FMM from Cheng et al (1999)
Connection between the FMM and Boundary Element Methods
12/02/03 Lecture 24 Some research ideas/directions. Review
12/04/03 Project Reports 1 1. Yang Wang: A Java-based animated implementation of the FMM in 2-D
2. Zhenyu Zhang: FMM for the solution of an eigenvalue problem for a surface integral operator in 3-D
3. Karthikeyan Duraisamy: Fast particle methods for the simulation and control of 3D Vortex Wakes from Lifting Wakes
4.
Zhiyun Li: Nonuniform Fast Fourier Transforms
12/09/03 Project Reports 2 5. Weigong Zhang: Fast summation of Helmholtz monopoles in 2-D.
6.  Alap Karapurkar:
The Fast Multipole Method for Diffuse Light Scattering
7. Shaju John and S. Koushik:
Simulation of ferromagnetic particle chain formation in a fluid medium under the action of a magnetic field
8: Shreyas Ananthan and Sandeep Gupta: Fast Multipole Methods for Particle Simulations in Vortex Dominated Flows

All project final reports are due on this day.

12/11/03 Final Solution

 

* These lectures have been distributed as hardcopy, since they are based on as yet unpublished research.