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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.
ECE 595E Lecture 36: MEEP Tutorial II
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30 Apr 2013 | Online Presentations | Contributor(s): Peter Bermel
Outline: Recap from Monday Examples Multimode ring resonators Isolating individual resonances Kerr nonlinearities Quantifying third-harmonic generation
ECE 595E Lecture 35: MEEP Tutorial I
18 Apr 2013 | Online Presentations | Contributor(s): Peter Bermel
Outline: MEEP Interfaces MEEP Classes Tutorial examples: Waveguide Bent waveguide
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 diverse …
[Illinois] An Overview of Multiscale Simulation Algorithms: Guidelines and Pitfalls to Avoid
29 Dec 2012 | Online Presentations | Contributor(s): Richard Braatz
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 that …
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 expressions Tight …
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. Learning Objectives: This lecture provides a very high level overview of quantum dots. The main issues and questions …
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: User requirements Graphical user interface Software structure Program developer requirements …
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 …
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 Topics: Reductions and Memory Patterns Reduction Patterns in CUDA Mapping Data into CUDA's Memories Input/Output Convolution Generic Algorithm …
Illinois ECE 498AL: Programming Massively Parallel Processors, Lecture 13: Reductions and their Implementation
15 Sep 2009 | Online Presentations | Contributor(s): Wen-Mei W Hwu
Structuring Parallel Algorithms Topics: Parallel Reductions Parallel Prefix Sum Relevance of Scan Application of Scan Scan on the CPU First attempt Parallel Scan Algorithm Work …
Illinois ECE 498AL: Programming Massively Parallel Processors, Lecture 12: Structuring Parallel Algorithms
Structuring Parallel Algorithms Topics: Key Parallel Programming Steps Algorithms Choosing Algorithm Structure Mapping a Divide and Conquer algorithm Tiled Algorithms Increased work …
Experiment vs. Modelling: What's the problem?
10 Aug 2009 | Online Presentations | Contributor(s): William L. Barnes
Progress in plasmonics has been greatly assisted by developments in experimental techniques and in numerical modelling. This talk will look at some of the difficulties that emerge when …
Quantitative, Kinetic Models of Cellular Circuits
04 Apr 2009 | Online Presentations | Contributor(s): Michael R. Brent
Living cells contain complex, analog circuits that regulate the rate at which each gene produces its product. The kinetic properties of these circuits enable cells to respond to changes in their …
The Multicore Era: Crisis or (and?) Opportunity?
27 Mar 2009 | Online Presentations | Contributor(s): Mithuna Thottethodi
This talk will provide a brief overview of how we got to the multicore era, the implications and challenges for hardware/software developers and users, and some informed speculation on where the …
Experiences with nonintrusive polynomial Chaos and stochastic collocation methods for uncertainty analysis and design
13 Mar 2009 | Online Presentations | Contributor(s): Michael S. Eldred
Non—intrusive polynomial chaos expansion (PCE) and stochastic collocation (SC) methods are attractive techniques for uncertainty quantification due to their abilities to produce functional …
Nanoparticle and Colloidal Simulations with Molecular Dynamics
05 Dec 2008 | Online Presentations | Contributor(s): Steve Plimpton
Modeling nanoparticle or colloidal systems in a molecular dynamics (MD) code requires coarse-graining on several levels to achieve meaningful simulation times for study of rheological and other …
25 Nov 2008 | Online Presentations | Contributor(s): Seung-Jai Min
This tutorial consists of three parts. First, we will discuss about how OpenMP is typically used and explain OpenMP programming model. Second, we will describe important OpenMP constructs and data …
Introduction to Parallel Programming with MPI
24 Nov 2008 | Online Presentations | Contributor(s): David Seaman
Single-session course illustrating message-passing techniques. The examples include point-to-point and collective communication using blocking and nonblocking transmission. One application …
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