University of Minnesota Supercomputer Institute

Seminar Synopses

Statistical Mechanics of Random Surfaces -- Daniel Kroll

The Effects of Lateral Viscosity Variations on 3-D Spherical Shell Mantle Convection -- Zhuxia Zhang

Parallel Direct Methods for Sparse Linear Systems -- Michael T. Heath

The Search for TeraFLOP: Massive Parallelism Meets Distributed Computing -- Robert Benner

Can Supercomputer-Assisted Cardiovascular Monitoring Prevent Catastrophic Disease-Stroke and Cardiac Death? -- Bohumil Fiser

Understanding Human Joint Mechanics Through Advanced Computational Models -- Robert Spilker

Computation of Viscoelastic Flows with Higher and Lower Order Finite Elements -- Bamin Khomami

Free Mesh FEM: A Kind of Meshless Scheme -- Genki Yagawa

Statistical Mechanics of Random Surfaces

Daniel Kroll
Department of Medicinal Chemistry
University of Minnesota

The behavior of many complex systems in physics, biology, and chemistry can be described in terms of the statistical mechanics of fluctuating surfaces. Prominent examples are the cell membranes of mammalian red blood cells, the interfaces between oil- and water-rich regions in microemulsions, and the worldsheets of strings in high-energy physics. In all these cases, the surface tension is either very small or vanishes identically, so that the structure and dynamics of these surfaces is determined by their elastic bending rigidity and shear modulus.

Recent progress in this field was reviewed. In particular, the phase diagram and scaling behavior of self-avoiding fluid vesicles was described. Also, it was shown how the interplay of entropy, bending rigidity, and pressure increment stabilize a number of structures.

The Effects of Lateral Viscosity Variations on 3-D Spherical Shell Mantle Convection

Shuxia Zhang
Department of Geology and Geophysics
University of Minnesota

Inclusion of strong lateral variations is a great challenge for modeling mantle convection because the viscosity of mantle rocks is strongly temperature-, pressure-, and stress-dependent and great mathematical difficulties arise from lateral viscosity variations. While convection models incorporating complex rheology in a Cartesian system are important for understanding the nature of mantle convection, their results cannot be compared directly to the data observed at the earth's surface because of their inappropriate geometry.

Using a 3-D spectral model, the speaker demonstrated a numerical strategy for handling the viscosity variations and showed the effects of lateral viscosity variations on convection platforms and heat transfer properties by comparing them to the convection models without lateral viscosity variations. Also, calculated results were compared with observational data, and dynamical implications of the numerical results were discussed.

Parallel Direct Methods for Sparse Linear Systems

Michael T. Heath
National Center for Supercomputing Applications
University of Illinois
Urbana, Illinois

Dr. Heath presented an overview of parallel direct methods for solving sparse systems of linear equations, focusing on symmetric positive definite systems. He examined the performance implications of the important differences between dense and sparse systems. His main emphasis was on parallel implementation of the numerically intensive factorization process and the associated triply nested loop required by the algorithm, but he also briefly considered the other major components of direct methods, such as parallel ordering. Additional topics included in the seminar included the multifrontal approach and the use of elimination trees.

The Search for TeraFLOP: Massive Parallelism Meets Distributed Computing

Robert Benner
Sandia National Laboratory
Computational Sciences & Mathematics Center
Albuquerque, New Mexico

There is considerable anticipation that 1995 might be the "Year of the TeraFLOP," i.e. one trillion sustained floating point operations per second on real applications.

Dr. Benner addressed several questions: How important is the TeraFLOPs milestone to parallel computing in general and the High Performance Computing and Communications Initiative in particular?; Under what conditions might TeraFLOPs be achieved for different classes of applications?; In addition to performance, are the most important problems in parallel computing being addressed?; and finally, What new roles might emerge for universities, national laboratories, and industry in the development of super-computing applications? Applications emphasized in this talk were Xpatch, a program for analyzing electromagnetic signatures from radar bounces; and CRADA, a multifrontal solver characterized by intensive communication needs.

Can Supercomputer-Assisted Cardiovascular Monitoring Prevent Catastrophic Disease-Stroke and Cardiac Death?

Bohumil Fiser

Dr. Fiser asked the question: Can we identify risk of sudden cardiac death by monitoring cardiovascular functions? He pointed out that the risk of sudden cardiac death can be determined by computation of the baroreflex sensitivity (BRS). BRS is determined by means of spectral analysis of blood pressure (BP) and heart rate fluctuations (obtained by using a non-invasive continuous three-minute record). A twenty-four hour record of BP should be preferable because of the circadian variations. For the correct diagnosis and treatment of hypertension, several days of BP monitoring are necessary. It was concluded that supercomputer-assisted cardiovascular monitoring can improve the intervention and decrease the risk of death and serious complications in patients with cardiovascular diseases.

Understanding Human Joint Mechanics Through Advanced Computational Models

Robert Spilker
Rensselaer Polytechnic Institute
Troy, New York

This lecture provided an overview of an interdisciplinary effort to develop automated and adaptive 3-D finite element analysis and parallel solution strategies to describe nonlinear moving contact problems characteristic of the biomechanics of joints in the human musculoskeletal system using the actual anatomic geometries and the multiphasic properties of the tissues in the joints. Dr. Spilker's work provides the sophisticated high-performance computational tools needed to make significant advances toward precise 3-D simulations of biomechanical problems related to diarthrodial joints, with realistic loading conditions, joint geometries, and constituent material properties. One example of the results obtained was a model of a shoulder joint with 20,000 degrees of freedom.

Computation of Viscoelastic Flows with Higher and Lower Order Finite Elements

Bamin Khomami
Department of Chemical Engineering
Stanford University
Stanford, California

The study of the mechanics of viscoelastic fluids is motivated by the need to understand complex flow phenomena involving materials characterized as non-Newtonian. Examples are the process of forming plastics, the flow of biological fluids, secondary recovery of oil and gases, and the processing of polymeric-based composite materials.

The speaker reviewed his research which demonstrates that domain decomposition spectral techniques provide a stable, convergent and cost efficient discretiz-ation of the set of equations governing flow of viscoelastic liquids. The talk also included a comparison of the performance of domain decomposition spectral techniques with specifically formulated lower-order finite element techniques. Namely, Elastic-Viscous Splitting of the Stress (EVSS), as well as EVSS/Streamline Upwind (SU), EVSS Streamline-Upwind Petrov-Galerkin Galerkin (SUPG), and higher-order Galerkin, in a number of viscoelastic flow problems.

Free Mesh FEM: A Kind of Meshless Scheme

Genki Yagawa
Department of Quantum Engineering and Systems Science
University of Tokyo
Tokyo, Japan

To efficiently simulate complicated physical phenomena, distributed parallel processing techniques are needed. To implement an analysis system which has the proper capabilities, techniques such as mesh generation, domain decomposition for load balancing, finite element analysis, posterior error estimation, and remeshing should be integrated into that system. However, this would make the finite element analysis system too complicated.

Dr. Yagawa has studied the meshless finite element methods in an attempt to reduce the complexity of such a system. This seminar presented a new meshless finite element method--Free Mesh FEM-- which is simple, accurate and suitable for parallel computing.