CSE Lecture Series

2005 Computational Science & Engineering (CSE) Lecture Series

June 23, 2005 - Prof. Gabriel Wittum

Large-Eddy Simulation with Parallel Adaptive Multigrid Methods
Thursday, June 23, 2005, 9:00 AM, Location: ICAM Conference Room, Wright House

Numerical simulation has become one of the major topics in Computational Science. To promote modelling and simulation of complex problems new strategies are needed allowing for the solution of large, complex model systems. Crucial issues for such strategies are reliability, efficiency, robustness, usability, and versatility.

After discussing the needs of large-scale simulation we point out basic simulation strategies such as adaptivity, parallelism and multigrid solvers. These strategies are combined in the simulation system UG (Unstructured Grids) being presented in the following.

Then we show the application of these strategies to the simulation of turbulent flows. In particular we present adaptive parallel methods for LES-type turbulence computations. Several dynamic subscale models are used and compared for typical benchmark problems. The suitability for complex configurations as used in practice is shown by computing an industrial mixing problem.

Finally, we present results of the parallel performance of our solver on System X.

June 23, 2005 - Prof. Michael Schäfer

Simulation of Coupled Fluid-Solid Problems
PART 1: Thursday, June 23, 2005, 11:00AM - 12:00noon (methods), Location: 117A Randolph Hall
PART 2: Thursday, June 23, 2005, 1:00PM - 2:00PM (applications), Location: 117A Randolph Hall

The numerical simulation of engineering applications in many cases requires the coupled solution of problems from structural mechanics, fluid mechanics, and/or heat transfer. Examples of such mechanically and/or thermally coupled fluid-solid problems can be found, for instance, in machine and plant building, engine manufacturing, turbomachinery, heat exchangers, offshore structures, chemical engineering processes, microsystem techniques, biology, or medicine.

The mini-lecture series addresses the most relevant aspects with respect to a reliable and efficient numerical simulation of such kind of coupled fluid-solid problems. After a classification of the corresponding problems with respect to different coupling mechanisms, a brief discussion of modeling aspects in the framework of continuum mechanics is given. As main part then numerical issues of discretization, grid dynamics, and solution procedures will be discussed. Here, special attention will be paid to the numerical realization of the coupling mechanisms, which is one of the crucial issues within any approach for the considered kind of problems. In particular, also the involvement of multigrid methods, which have proven to work very efficiently for individual fluid or solid problems, will be addressed.

By considering a variety of examples of applications involving different mechanical and thermal couplings aspects of reliability, computational efficiency, and numerical accuracy will be discussed.


Numerical Simulation and Optimization of Complex Flows: Status and Trends
Thursday, June 23, 2005, 4:00PM - 5:00PM, Location: 117A Randolph Hall

The lecture will give a survey on actual developments in the area of numerical simulation and optimization of flow problems. In particular, questions of reliability and efficiency of corresponding numerical approaches will be addressed. Different components of numerical methods for discretization, solution, and optimization --- including recent own developments --- will be presented and discussed to this respect. One focus will be on the "interaction" of the numerical schemes with the problem of handling the turbulence of flows, which still must be considered as a big challenge. Characteristic effects will be illustrated by results for concrete examples of applications also indicating the capabilities of the approaches considered.

June 15-16, 2005 - Matthias Heinkenschloss

Domain Decomposition Preconditioners for PDE Constrained Optimization
June 16, 4:00 - 6:00 PM, McBryde 455

Optimization problems governed by partial differential equations (PDEs) arise in many science and engineering applications, e.g., in the form of optimal control, optimal design and parameter identification problems. The solution of these problems presents many challenges. In this talk I will briefly discuss some PDE constrained optimization problems and then focus on domain decomposition preconditioners which are used as subproblem solvers within optimization algorithms.

The domain decomposition preconditioners are design for linear-quadratic elliptic and parabolic optimal control problems. They are applied on the optimization level and require the parallel solution of smaller optimal control problems posed on subdomains. I will discuss the derivation of domain decomposition preconditioners, present theoretical convergence results and illustrate their performance on example problems. I will briefly outline the possible application of these domain decomposition methods, coupled with model reduction for the design of in-network processing algorithms for sensor nets.

June 8-10, 2005 - Prof. Robert Harrison

Multiresolution Quantum Chemistry
Wednesday, June 8th at 11:00 am: Fralin Auditorium


High-performance computational chemistry: NWChem and Global Arrays
Thursday, June 9th at 11:00 am: Chemistry/Physics 140

May 2-6, 2005 - Karen Willcox

Lecture 1, Model Reduction for Large-Scale Systems

Lecture 2, The Proper Orthogonal Decomposition for Model Reduction of Large-Scale Systems

Lecture 3, Fourier Model Reduction

April 25-29, 2005 - Workshop on Compatible and Alternative Spatial Discretizations for PDE's

Pavel Bochev

Variational and geometric aspects of compatible discretizations
Monday 25 April, 2:30pm, McBryde 655

On least-squares principles for the Poisson equation and their connection to the Dirichlet and Kelvin principles, or how to do least-squares finite elements right
Wednesday 27 April, 2:30pm McBryde 655

Max Gunzburger

Color printers, mailboxes, fish, and Homer Simpson - or - Centroidal Voronoi tessellations; algorithms and applications
Monday 25 April, 4:00pm, Torgerson 1060

Finite element methods based on least-squares and modified variational principles
Tuesday 26 April, 2:00pm, McBryde 216

Least-squares finite element methods for optimal design and control problems
Thursday 28 April, 2:00 pm, McBryde 216

John Burkhardt

The Water Pump and the Spitting Fish
Tuesday 26 April, 5:30pm, McBryde 455

April 11-15, 2005 - Linda Petzold

Bridging the Scales in Biochemical Simulation (PDF; 13.5 MB)

The Coming Age of Computational Science (PDF; 2.2 MB)

Yang Cao

Multiscale Stochastic Simulation of Biochemical Systems

April 4-8, 2005 - Satya Atluri

Title: My current Research on the Meshless Local Petrov-Galerkin (MLPG) Method

March 14-16, 2005 - David Keyes

Scientific Discovery through Advanced Computing

March 2, 2005 - Eric de Sturler

Fast Solvers for Long Sequences of Linear Systems
Math Commons Room, 455 McBryde Hall

Many problems in science and engineering require the solution of a long sequence of linear systems with small changes from one matrix to the next but substantial changes over multiple systems. We are particularly interested in cases where both the matrix and the right hand side change and systems are not available simultaneously. Such sequences arise in time-dependent problems, nonlinear systems of equations and optimization, (distributed) parameter identification for inverse problems, and many other problems. We can significantly reduce the cost of solving subsequent systems in the sequence by recycling small selected subspaces of the search spaces from previous linear systems.

I will start with a brief introduction on iterative methods for large sparse linear systems and recent developments in the field. After that I will describe how we can adapt recently proposed methods to efficiently solve sequences of thousands of linear systems. This research brings together topics in the convergence analysis of iterative methods, perturbation theory for various properties of matrices, such as invariant subspaces, and using application and (nonlinear) algorithm features for tuning linear solvers.

I will demonstrate the effectiveness of the approach using results from crack propagation, diffuse optical tomography, and topology optimization. Other applications/collaborations include nonlinear mechanics and fatigue, materials science, and electro-magnetics.