Abstract : Remarkable progress has been made in recent years on multiscale modeling and computational methods for diverse problems in material sciences, including but not limited to fluid mechanics, pattern formation and defects in materials sciences, and soft and active materials in biology.
The research is interdisciplinary, spanning the fields of mathematics, materials science and biology. This minisymposium focuses on the recent progress in the multiscale modeling, mathematical analysis and computational methods of broad topics in material sciences. We aim to bring together experts from diverse fields to share their interesting research topics and recent progress and to promote interdisciplinary research collaborations.
[05618] On median filters for motion by mean curvature
Format : Talk at Waseda University
Author(s) :
Selim Esedoglu (University of Michigan)
Abstract : The median filter scheme is an elegant, monotone discretization of the level set formulation of motion by mean curvature. It turns out to evolve every level set of the initial condition by another class of methods known as threshold dynamics. Based on this connection, we revisit median filters in light of recent work on the threshold dynamics method.
[05389] Optimal error estimate for the Multiscale Finite Element Method
Format : Talk at Waseda University
Author(s) :
Pingbing Ming (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
Siqi Song (Academy of Mathematics and Systems Science)
Abstract : We derive the optimal energy error estimate for multiscale finite element method with oversampling technique applying to elliptic systems with rapidly oscillating periodic coefficients that are bounded and measurable, which may admit rough microstructures. As a by-product of the energy estimate, we derive the rate of convergence in
L$^{d/(d-1)}-$norm with $d$ the dimensionality.
[02920] Structure-preserving methods based on minimizing movement scheme for gradient flows with respect to transport distances
Format : Talk at Waseda University
Author(s) :
Chaozhen Wei (University of Electronic Science and Technology of China)
Abstract : I will present a novel structure-preserving numerical method for gradient flows w.r.t Wasserstein-like transport distances induced by concentration-dependent mobilities, which arise widely in materials science and biology. Based upon the minimizing movement scheme and modern operator-splitting schemes, our method has built-in positivity or boundedness preserving, mass conservation, and energy-dissipative structures. I will show the flexibility and performance of our methods through simulation examples including different free energy functionals, general wetting boundary conditions and degenerate mobilities.
[01430] A Continuum Model for Dislocation Climb Velocity and Numerical Simulations
Format : Talk at Waseda University
Author(s) :
Chutian Huang (Hong Kong University of Science and Technology)
Yang Xiang (Hong Kong University of Science and Technology)
Abstract : Dislocations are primary carriers for the crystal plastic deformation. The study of dislocation climb plays an important role in understanding plastic deformation of crystalline deformation at high temperature. In this work, we propose a new continuum formulation for dislocation climb velocity. Numerical simulations are implemented to compare our model with mobility law and discrete model.
[05350] Multi-scale modeling and simulations for two-phase flow with moving contact lines
Format : Talk at Waseda University
Author(s) :
Xianmin Xu (Chinese Academy of Sciences)
Abstract : Two phase flow with moving contact lines is very difficult to model and simulate due to its multi-scale nature. The slipness of the fluid molecules on solid substrates must be take into account near the contact line in a continuum model since the standard no slip boundary condition induces infinite energy dissipations. The microscopic roughness and inhomogeneity of the substrates make the problem even more challenging. In this talk, we will present some recent efforts to develop coarse-graining boundary condition and efficient numerical methods on the problem. In particular, we show that the Onsager principle can be used as an approximation tool to derive effective models for the dynamical multiscale problem.
[04103] Energy stable methods for two-phase phase-field surfactant model
Format : Talk at Waseda University
Author(s) :
Zhen Zhang (Southern University of Science and Technology)
Abstract : We develop energy stable and bound preserving schemes for phase-field surfactant model with moving contact lines. The desired properties of the schemes are rigorously proved. We numerically validate the accuracies of the schemes and apply them in simulating droplet impact problems. Qualitative agreements with experiments are obtained. Moreover, surfactants are observed to have effects on enhancing droplet deformation and reducing dissipations.
[01396] Construction and Analysis for the Coupling Method of Atomistic and Higher Order Continuum Models
Format : Talk at Waseda University
Author(s) :
Hao Wang (Sichuan University)
Yangshuai Wang (University of British Columbia)
Abstract : Atomistic to continuum coupling methods have been widely used in the numerical simulation of crystal lattice with defects. In this talk, we present the construction and analysis of a coupling scheme that combines the atomistic model with a higher order continuum with sharp interface. We show that such scheme is of higher order of accuracy compared with existing models that couples the atomistic model with the classic Cauchy-Born model.
[01316] A domain decomposition method for the Poisson-Boltzmann solvation model
Format : Talk at Waseda University
Author(s) :
Chaoyu Quan (Southern University of Science and Technology)
Abstract : A nonoverlapping domain decomposition method is studied for the linearized Poisson--Boltzmann equation, which is essentially an interior-exterior transmission problem with bounded interior and unbounded exterior. This problem is different from the classical Schwarz alternating method for bounded nonoverlapping subdomains well studied by Lions in 1990, and is challenging due to the existence of unbounded subdomain. To obtain the convergence, a new concept of interior-exterior Sobolev constant is introduced and a spectral equivalence of related Dirichlet-to-Neumann operators is established afterwards. We prove rigorously that the spectral equivalence results in the convergence of interior-exterior iteration. Some numerical simulations are provided to investigate the optimal stepping parameter of iteration and to verify our convergence analysis.
[05400] Numerical methods for topology optimization and applications
Format : Online Talk on Zoom
Author(s) :
Xiaoping Wang (Hong Kong university of science and technology)
Abstract : n this talk, I will introduce some numerical methods for topology optimization based on threshold dynamics method. Applications to linear elasticity, fluid network and porous media problems will be discussed.
