Lew Lefton

Penalty finite element approximations of the stationary power-law Stokes problem

Finite element approximations of the stationary power-law Stokes problem using penalty formulation are considered. A priori error estimates under appropriate smoothness assumptions on the solutions are established without assuming a discrete version of the BB condition. Numerical solutions are presented by implementing a nonlinear conjugate gradient method.

Optimal numerical flux of power-law fluids in some partially full pipes

Consider the steady state pressure driven flow of a power-law fluid in a partially filled straight pipe. It is known that an increase in flux can be achieved for a fixed pressure by partially filling the pipe and having the remaining volume either void or filled with a less viscous, lubricating fluid. If the pipe has circular cross section, the fluid level which maximizes flux is the level which avoids contact with exactly 25% of the boundary. This result can be proved analytically for Newtonian fluids and has been verified numerically for certain non-Newtonian models. This paper provides a generalization of this work numerically to pipes with non-circular cross sections which are partially full with a power-law fluid. A simple and physically plausible geometric condition is presented which can be used to approximate the fluid level that maximizes flux in a wide range of pipe geometries. Additional increases in flux for a given pressure can be obtained by changing the shape of the pipe but leaving the perimeter fixed. This computational analysis of flux as a function of both fluid level and pipe geometry has not been considered to our knowledge. Fluxes are computed using a special discretization scheme, designed to uncover general properties which are only dependent on fluid level and/or pipe cross-sectional geometry. Computations use finite elements and take advantage of the variational structure inherent in the power-law model. A minimization technique for approximating the critical points of the associated non-linear energy functional is used. In particular, the numerical scheme for the non-linear partial differential equation has been proved to be convergent with known error estimates. The numerical results obtained in this work can be useful for designing pipes and canals for transportation of non-Newtonian fluids, such as those in chemical engineering and food processing engineering.

Special session — Improvisation methods to catalyze engineering creativity

Numerous organizations, including the National Science Board and the National Academy of Engineering recognize the importance of creativity and innovation in the Engineering field. However, there is very little activity focused on systematically inserting these important concepts into engineering design and engineering education. The proposed workshop utilizes a systematic approach that is currently part of an ongoing research project to develop a protocol for engineering innovation and implement this in the engineering classroom. This protocol uses humorous improvisation techniques to generate technical design solutions. It uses improvisation as a random idea generator as a random number generator is often used in stochastic simulation. Unlike previous applications of improvisation to innovation, this protocol is suitable to technical applications because it utilizes an additional step to produce technical solutions from random improvised ideas. The workshop is intended for engineers or engineering students that wish to increase the innovativeness of their engineering design. It is also intended for engineering educators who wish to incorporate this innovation protocol into their design courses.

An Introduction to Parallel and Vector Scientific Computing: Contents

Part I. Machines and Computation: 1. Introduction - the nature of high performance computation 2. Theoretical considerations - complexity 3. Machine implementations Part II. Linear Systems: 4. Building blocks - floating point numbers and basic linear algebra 5. Direct methods for linear systems and LU decomposition 6. Direct methods for systems with special structure 7. Error analysis and QR decomposition 8. Iterative methods for linear systems 9. Finding eigenvalues and eigenvectors Part III. Monte Carlo Methods: 10. Monte Carlo simulation 11. Monte Carlo optimization Appendix: programming examples.

An Introduction to Parallel and Vector Scientific Computing: APPENDIX: PROGRAMMING EXAMPLES

Part I. Machines and Computation: 1. Introduction - the nature of high performance computation 2. Theoretical considerations - complexity 3. Machine implementations Part II. Linear Systems: 4. Building blocks - floating point numbers and basic linear algebra 5. Direct methods for linear systems and LU decomposition 6. Direct methods for systems with special structure 7. Error analysis and QR decomposition 8. Iterative methods for linear systems 9. Finding eigenvalues and eigenvectors Part III. Monte Carlo Methods: 10. Monte Carlo simulation 11. Monte Carlo optimization Appendix: programming examples.

An Introduction to Parallel and Vector Scientific Computing: MACHINES AND COMPUTATION

Part I. Machines and Computation: 1. Introduction - the nature of high performance computation 2. Theoretical considerations - complexity 3. Machine implementations Part II. Linear Systems: 4. Building blocks - floating point numbers and basic linear algebra 5. Direct methods for linear systems and LU decomposition 6. Direct methods for systems with special structure 7. Error analysis and QR decomposition 8. Iterative methods for linear systems 9. Finding eigenvalues and eigenvectors Part III. Monte Carlo Methods: 10. Monte Carlo simulation 11. Monte Carlo optimization Appendix: programming examples.

An Introduction to Parallel and Vector Scientific Computing: LINEAR SYSTEMS

Part I. Machines and Computation: 1. Introduction - the nature of high performance computation 2. Theoretical considerations - complexity 3. Machine implementations Part II. Linear Systems: 4. Building blocks - floating point numbers and basic linear algebra 5. Direct methods for linear systems and LU decomposition 6. Direct methods for systems with special structure 7. Error analysis and QR decomposition 8. Iterative methods for linear systems 9. Finding eigenvalues and eigenvectors Part III. Monte Carlo Methods: 10. Monte Carlo simulation 11. Monte Carlo optimization Appendix: programming examples.

An Introduction to Parallel and Vector Scientific Computing: Index

Part I. Machines and Computation: 1. Introduction - the nature of high performance computation 2. Theoretical considerations - complexity 3. Machine implementations Part II. Linear Systems: 4. Building blocks - floating point numbers and basic linear algebra 5. Direct methods for linear systems and LU decomposition 6. Direct methods for systems with special structure 7. Error analysis and QR decomposition 8. Iterative methods for linear systems 9. Finding eigenvalues and eigenvectors Part III. Monte Carlo Methods: 10. Monte Carlo simulation 11. Monte Carlo optimization Appendix: programming examples.

An Introduction to Parallel and Vector Scientific Computing: Frontmatter

Part I. Machines and Computation: 1. Introduction - the nature of high performance computation 2. Theoretical considerations - complexity 3. Machine implementations Part II. Linear Systems: 4. Building blocks - floating point numbers and basic linear algebra 5. Direct methods for linear systems and LU decomposition 6. Direct methods for systems with special structure 7. Error analysis and QR decomposition 8. Iterative methods for linear systems 9. Finding eigenvalues and eigenvectors Part III. Monte Carlo Methods: 10. Monte Carlo simulation 11. Monte Carlo optimization Appendix: programming examples.

An Introduction to Parallel and Vector Scientific Computation

Part I. Machines and Computation: 1. Introduction - the nature of high performance computation 2. Theoretical considerations - complexity 3. Machine implementations Part II. Linear Systems: 4. Building blocks - floating point numbers and basic linear algebra 5. Direct methods for linear systems and LU decomposition 6. Direct methods for systems with special structure 7. Error analysis and QR decomposition 8. Iterative methods for linear systems 9. Finding eigenvalues and eigenvectors Part III. Monte Carlo Methods: 10. Monte Carlo simulation 11. Monte Carlo optimization Appendix: programming examples.