Abstract: Fractional diffusion equations provide an adequate and accurate description of transport processes that exhibit anomalous diffusion that is characterized by an algebraically decaying detail of the corresponding probability density function. Computationally, because of the nonlocal property of fractional differential operators, the numerical methods for fractional diffusion equations often generate dense coefficient matrices. Consequently, these methods often require computational work of O(N3) to invert per time step and memory of O(N2) for where N is the number of unknowns. Furthermore, fractional diffusion equations with smooth coefficients may generate solutions with strongly local behavior. Mathematically, fractional differential equations exhibit mathematical properties that have fundamental differences from those of integer-order differential equations.

In this talk we go over the recent developments of accurate and efficient numerical methods for space-fractional partial differential equations. These methods have computational cost of O(N log2 N) per time step and memory of O(N), while retaining the same accuracy and approximation property of the underlying numerical methods. We will also address mathematical issues on the space-fractional differential equations such as wellposedness and regularity of the problems and their impact on the convergence behavior of numerical methods. We will report our recent progress in this direction.

 

About the Speaker: Professor Hong Wang has been working on numerical methods and computational techniques for partial differential equations and corresponding numerical and mathematical analysis. His research primarily focuses on the fields of porous medium flow and transport as well as fractional partial differential equations and related nonlocal problems.

 

Date&Time: December 26, 2014 (Friday), 9:30 - 11:30 a.m.
Location: 606 Conference Room