北京科学与工程计算研究院2017暑期学术研讨会

Date: 2017.8.1

Time:10:00-10:40

Venue:M842, 8th floor, BISEC

Speaker:Philippe Devloo, Department of Civil Engineering, Architecture and Urbanism at the State University of Campinas, Brazil

Title: MHM Approximations using H 1 and H( div ) approximations

Abstract:

The multi scale hybrid method is a numerical technique developed by Paredes, Valentin and Harder aimed at approximating problems with multiple scales. In this talk we present numerical simulations using the MHM numerical technique as well as an extension of MHM where mixed approximations are used in the interior of the macro domains.

The resulting technique named MHM-(div) has improved approximation qualities and results in a numerical method that is locally conservative. This feature makes MHM-H(div) suitable to model transport problems typical for reservoir simulation.

Date:  2017.8.1

Time: 10:40-11:20

Venue: M842, 8th floor, BISEC

Speaker:Xiaofeng Yang, Department of Mathematics, University of South Carolina, USA

Title: IEQ approach — A novel numerical approach to solve the Gradient flow problem with high nonlinearity

Abstract:
The free energies of gradient flow systems usually consist of various nonlinear potentials formulated in diverse complex formats which present a major challenge in the construction of efficient and accurate time discretization schemes. We overcome this challenge by developing a flexible and robust IEQ approach which enables us to develop time discretization schemes for a large class of gradient flow systems. More precisely, the developed schemes (i) are accurate (up to second order in time); (ii) are stable (unconditional energy dissipation law holds); and (iii) are efficient and easy  to implement (only need to solve some positive definite linear system at each time step.

Date:  2017.8.1

Time: 11:20-12:00

Venue: M842, 8th floor, BISEC

Speaker: Huayi Wei, School of Mathematics and Computational Science, Xiangtan University, CHINA

Title:An interface-fitted mesh generator and virtual element methods for elliptic interface problems

Abstract:

A simple and efficient interface-fitted mesh generation algorithm which can produce a semi-structured interface-fitted mesh in two and three dimensions quickly is developed in this paper. Elements in such interface-fitted meshes are not restricted to simplices but can be polygons or polyhedra. Especially in 3D, the polyhedra instead of tetrahedra can avoid slivers. Virtual element methods are applied to solve elliptic interface problems with solutions and flux jump conditions. Algebraic multigrid solvers are used to solve the resulting linear algebraic system. Numerical results are presented to illustrate the effectiveness of our method.