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Whether you're simulating the electronic structure of a carbon nanotube or the strain within an automobile part, the
calculations usually boil down to a simple matrix equation,
Ax = f. The faster you can fill the
matrix A with the coefficients for your partial
differential equation (PDE), and the faster you can solve for
the vector x given a forcing function f, the faster you have your overall solution. Things get interesting when the matrix A is too large to fit in the memory available on one machine, or when the coefficients in A cause the matrix to be ill-conditioned.
Ax = f
Many different algorithms have been developed to map a PDE onto a matrix, to pre-condition the matrix to a better form, and to solve the matrix with blinding speed. Different algorithms usually exploit some property of the matrix, such as symmetry, to reduce either memory requirements or solution speed or both.
Learn more about algorithms from the many resources on this site, listed below.
Data-Centric Models for Multilevel Algorithms
07 Feb 2016 | Online Presentations | Contributor(s): Samuel Guiterrez
Today, computational scientists must contend with a diverse set of supercomputer architectures that are capable of exposing unprecedented levels of parallelism and complexity. Effectively placing,...
Range Decomposition: A Low Communication Algorithm for Solving PDEs on Massively Parallel Machines
07 Feb 2016 | Online Presentations | Contributor(s): Tom Manteuffel
The Range Decomposition (RD) algorithm uses nested iteration and adaptive mesh refinement locally before performing a global communication step. Only several such steps are observed to be...
A Scalable Algorithm for Inverse Medium Problems with Multiple Sources
04 Feb 2016 | Online Presentations | Contributor(s): Keith Kelly
We consider the problem of acoustic scattering as described by the free-space, time-harmonic scalar wave equation given...
ECE 595E Lecture 36: MEEP Tutorial II
30 Apr 2013 | Online Presentations | Contributor(s): Peter Bermel
Recap from Monday
Multimode ring resonators
Isolating individual resonances
Quantifying third-harmonic generation
Integrated Imaging Seminar Series
30 Apr 2013 | Series | Contributor(s): Charles Addison Bouman
Integrated imaging seminar series is jointly sponsored by the Birck Nanotechnology Center and ECE. Integrated Imaging is defined as a cross-disciplinary field combining sensor science, information...
ECE 595E Lecture 35: MEEP Tutorial I
18 Apr 2013 | Online Presentations | Contributor(s): Peter Bermel
Data-adaptive Filtering and the State of the Art in Image Processing
15 Apr 2013 | Online Presentations | Contributor(s): Peyman Milanfar
In this talk, I will present a practical and unified framework for understanding some common underpinnings of these methods. This leads to new insights and a broad understanding of how these...
ECE 595 Course Policy - Spring 2013
03 Jan 2013 | Teaching Materials | Contributor(s): Peter Bermel
A description of the key policies that will govern the administration of ECE 595 on "Numerical Methods" in Spring 2013.
The Pioneers of Quantum Computing
19 Nov 2010 | Online Presentations | Contributor(s): David P. Di Vincenzo
This talk profiles the persons whose insights and visions created the subject of quantum information science. Some famous, some not, they all thought deeply about the puzzles and contradictions...
Nanoelectronic Modeling Lecture 29: Introduction to the NEMO3D Tool
04 Aug 2010 | Online Presentations | Contributor(s): Gerhard Klimeck
This presentation provides a very high level software overview of NEMO3D. The items discussed are:
Modeling Agenda and Motivation
Tight-Binding Motivation and basic formula...
Nanoelectronic Modeling Lecture 28: Introduction to Quantum Dots and Modeling Needs/Requirements
20 Jul 2010 | Online Presentations | Contributor(s): Gerhard Klimeck
This presentation provides a very high level software overview of NEMO1D.
This lecture provides a very high level overview of quantum dots. The main issues and...
Nanoelectronic Modeling Lecture 26: NEMO1D -
09 Mar 2010 | Online Presentations | Contributor(s): Gerhard Klimeck
NEMO1D demonstrated the first industrial strength implementation of NEGF into a simulator that quantitatively simulated resonant tunneling diodes. The development of efficient algorithms that...
Nanoelectronic Modeling Lecture 27: NEMO1D -
This presentation provides a very high level software overview of NEMO1D. The items discussed are:
Graphical user interface
Nanoelectronic Modeling Lecture 21: Recursive Green Function Algorithm
07 Feb 2010 | Online Presentations | Contributor(s): Gerhard Klimeck
The Recursive Green Function (RGF) algorithms is the primary workhorse for the numerical solution of NEGF equations in quasi-1D systems. It is particularly efficient in cases where the device is...
Lecture 6: Neighbor Lists
05 Jan 2010 | Presentation Materials | Contributor(s): Ashlie Martini
Saving simulation time
Lecture 3: Integration Algorithms
Short Course on Molecular Dynamics Simulation
13 Oct 2009 | Courses | Contributor(s): Ashlie Martini
This set of ten presentations accompanied a graduate level course on Molecular Dynamics simulation. The specific objective of the course (and the presentations) is to provide:
1. Awareness of...
Illinois ECE 498AL: Programming Massively Parallel Processors, Lecture 15: Kernel and Algorithm Patterns for CUDA
30 Sep 2009 | Online Presentations | Contributor(s): Wen-Mei W Hwu
Kernel and Algorithm Patterns for CUDA
Reductions and Memory Patterns
Reduction Patterns in CUDA
Mapping Data into CUDA's Memories