MS-Th-BC-32
Structured-mesh methods for interface problems. - Part IV of VII
For Part I, see MS-Tu-E-32
For Part II, see MS-We-D-32
For Part III, see MS-We-E-32
For Part V, see MS-Th-D-32
For Part VI, see MS-Th-E-32
For Part VII, see MS-Fr-D-32

Date: August 13
Time: 10:00--12:00
Room: 307A

(Note: Click title to show the abstract.)

Organizer:
Chen, Huanzhen (College of Mathematical Sci. Shandong Normal Univ.)
He, Xiaoming (Missouri Univ. of Sci. & Tech.)
KWAK, Do Young (Korea Advanced Inst. of Sci. & Tech.)
Zhang, Xu (Purdue Univ.)

Abstract: In many real world applications it is more convenient or efficient to utilize structured meshes for solving different types of interface problems. Since the structured meshes may not fit the non-trivial interfaces, special methods need to be developed to deal with the difficulties arising from the interface problems in order to solve them on these meshes. Therefore, great efforts have been made for solving interface problems and tracing the moving interfaces based on structured meshes in the past decades. This mini-symposium intends to create a forum for researchers from different fields to discuss recent advances on the structured-mesh numerical methods for interface problems and their applications.

MS-Th-BC-32-1
10:00--10:30
Adaptive Finite Element Algorithms for Structured-mesh Methods for Interface Problems
Zhang, Shun (City Univ. of Hong Kong)
Abstract: In this talk, we will talk about a posteriori error estimates and adaptive algorithms for structured-mesh methods for interface problems. For interface problems, immersed finite elements can handle the un-alignment of interface and computational grids well. On the other hand, such problems often have low regularity near the intersections of interfaces, which need adaptive refinements to handle. We will discuss algorithms combining these two features.

MS-Th-BC-32-2
10:30--11:00
Second-order partitioned time stepping method for fluid-fluid interaction
Zheng, Haibiao (East China Normal Univ.)
Abstract: We study a second-order partitioned time stepping method( BDF2-GA(AB2)) for fluid-fluid interaction. This is accomplished through explicit treating the jump in velocities across the fluid-fluid interface by a geometric averaging of this data over the Adams-Bashforth formulation with the previous two time levels.

MS-Th-BC-32-3
11:00--11:30
Computation of the Schroedinger equation in the semiclassical regime on unbounded domain
Jiwei, Zhang (Beijing Computational Sci. Research Center)
YANG, XU (Univ. of California, Santa Barbara)
Abstract: The study of this paper is two-fold: (1) local absorbing boundary conditions (ABCs) are generlized to compute the Schroedinger equation on unbounded domain; then (2) a new asymptotic method based on the frozen Gaussian approximation. The ABCs are dealt that all effects of the Gaussian functions which contribute to the outgoing waves will be eliminated by stopping Hamiltonian flow of their centers when they get out of the domain of interest.

MS-Th-BC-32-4
11:30--12:00
Immersed Finite Element Methods for Interface Problems
Lin, Tao (Mathematics)
He, Xiaoming (Missouri Univ. of Sci. & Tech.)
Abstract: This is a brief introduction to immersed finite element (IFE) methods which can use interface-independent (Cartesian) meshes to solve interface problems even for interfaces with non-trivial geometries. Starting with basic ideas of IFE methods, we will discuss fundamental analysis for IFE methods, highlighting some essential differences between FE and IFE methods. We will then illustrate features of IFE methods with applications. We will conclude with a list of future research topics for IFE methods.

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