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Eberly College of Science Mathematics Department

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August 5th, 2014 (11:00am - 12:50pm)
Seminar: Ph.D. Thesis Defense
Title: "The auxiliary space technique for linear solvers"
Speaker: Lu Wang, Adviser: Jinchao Xu, Penn State
Location: MB106

Developing efficient iterative methods and parallel algorithms for solving sparse linear systems discretized partial differential equations (PDEs) is still a challenging tasks in scientific computing and practical applications. Though many mathematically optimal solvers such as the multigrid method have been developed, the unfortunate reality is that multigrid methods have not been much used in practical applications. Based on the methodology of Fast Auxiliary Space Preconditioning (FASP), we develop formulate and analyze preconditioning techniques that will narrow the gap between theory and practice, specifically by developing mathematically optimal solvers that are robust and easy to use in practice. A new parallel unsmoothed aggregation algebraic multigrid (UA-AMG) method for a PDE defined on an unstructured from the hierarchical structured coarse grid. It provides (nearly) optimal load balance and predictable communication patterns factors that make our new algorithm suitable for parallel computing. We will also try to extend the FASP techniques to saddle point and indefinite problems. Finally we present applications and show results from several application areas.

August 15th, 2014 (10:00am - 11:30am)
Seminar: Complex Fluids Seminar
Title: Cavity Computation in Nonlinear Elasticity
Speaker: Zhiping Li, Peking University
Location: MB106
Abstract: http://www.personal.psu.edu/txh35/LiZHP.pdf
August 18th, 2014 (10:00am - 11:30am)
Seminar: Complex Fluids Seminar
Title: : Large time blow up for a perturbation of the cubic Szegő equation
Speaker: Haiyan Xu, University Paris-Sud 11
Location: MB106

I am going to discuss a pertubed cubic Szegő equation i u_t = Pi (|u|^2u) + α (u|1) on the circle, where Pi is the Szegő projector on non-negative frequencies. This equation with α=0 was recently introduced as a toy model for totally non dispersive evolution equations by P. Gerard (Paris-Sud University, Orsay, France) and S. Grellier (University of Orleans, France). It is globally well-posed with a Lax pair structure for any real number α. Given initial data in a special subset of rational functions, the solutions stay in a relatively compact subset of trajectories for α<0. While for α> 0, there exist trajectories on which high Sobolev norms exponentially grow with time.

August 26th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: An introduction to the use of algebraic geometry I ATTENTION: the second lecture in this series will take place on THURSDAY AUGUST 28 3:30-6pm n Teichmuller dynamics,I
Speaker: Alex Wright, Stanford University
Location: MB216
August 27th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: When Group Work Fails
Speaker: Attendees, Penn State
Location: MB102

Group projects are lauded for their ability to teach students various skills important to professional work, including communication, management, and planning. But not all group work is successful. In some cases, members of a group may put in less work or no work at all. This week, we read a summary of literature from social psychology on this topic and discuss strategies to combat this phenomenon.
Myers, David G. "Many Hands Make Diminished Responsibility." Exploring Social Psychology. 6th ed. New York: McGraw-Hill, 1994. 203-08. Print.