Abstract: In this talk, we shall

present a pseudo-spectral multiscale method (PMM). More precisely, we derive a

coarse grid equation for mean displacement by a matching di erential operator

approach. This equation accurately and efficiently describes averaged motion

away from MD region. Meanwhile, we compute detailed dynamics from the Newton law in MD region.

Boundary conditions on interfaces are provided through defining displacement at

ghost point atoms. We reassign coarse grid displacement by averaging this

detailed solution in MD region. To get ghost point atom displacement, we make a

spectral decomposition of displacement. Total displacement is split into mean

part and fine fluctuation part. The coarse grid solution helps identifying mean

displacement at both interfacial atoms and ghost point atoms. This make our

algorithm a pseudo-spectral method. Fine fluctuation at ghost point atoms are

reconstructed through convolving time history kernel function with fine

fluctuation at neighboring interfacial atoms.

Major

error source in this type of multiscale method lies in energy interchange

between mean displacement and fine fluctuation across the interfaces.

Mismatching in interface then produces reflection towards the MD regions. In

PMM, we considerably reduce such interchange by spectral decomposition, and cut

mismatching by time history kernel treatment. Due to this balanced

considerations on interfacial conditions and coarse grid and fine grid schemes,

global multiscale resolution is reached. Numerical simulations have manifested

the efficiency and accuracy.

This

talk is based on joint works with Professors Thomas Y. Hou and Wing Kam Liu.

This multiscale method has been motivated by the Bridging Scale

Method.

唐少强，1995年于香港科大获博士学位（数学），主要从事计算力学与应用数学的研究，包括流体不稳定性与耗散的非线性相互作用、相变演化、半导体载流子输运、多尺度方法等。现任北京大学力学与工程科学系教授。

清华大学周培源应用数学研究中心

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