两类相场模型的高效自适应方法研究

项目名称： 两类相场模型的高效自适应方法研究

项目编号： No.11271350

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 张鉴

作者单位： 中国科学院计算机网络信息中心

项目金额： 68万元

中文摘要： 相场模型具有隐式追踪界面和基于能量变分的特点，被广泛应用在合金微结构演化、化学反应、高分子构象变化等等多个方面。为保证模拟结果具有良好的统计性，需采用大尺度、长时间的模拟。传统的均匀网格离散方法效率低；显式时间积分格式时间步长受相场方程的刚性、算法稳定性的限制强。自适应网格的离散可以提高网格效率，半隐式和隐式的时间积分格式可以放松稳定性限制。因此自适应方法和半隐式、隐式时间积分格式是目前相场模型算法研究的主流。我们将依托在这些方面的研究基础和申请支撑单位强大的算法设计实现以及计算能力；针对相场模型鞍点问题和弹性应变能与自适应方法结合的国际前沿问题；基于综合考虑模型、时间和空间误差的思想；采取由简到繁、由易到难的策略进行相场模型高效自适应（半）隐式算法的研究，既有创新性又有实用性。对于相场模型自适应算法理论、相场模拟效率的提高和应用的扩展都具有重要的理论和实践上的指导意义。

中文关键词： 相场；过渡态；自适应；大时间步长；超大规模并行

英文摘要： Phase field method is an energy-variation approach with the feature of implicit interface tracking. It is broadly used in many areas such as micro-structure evolution in alloys, chemical reaction, comformational change in macromolecules and so on. Large spatial and temporal scale simulations are usually required in these applications to ensure statistical reliability. However, the traditional uniform mesh discretization is inefficient and the time-step length of explicit time stepping scheme is limited severely by the stiffness of phase field equations. In order to improve the discretization efficiency and relax the stability constraint on time step length, the research has been focused on adaptive methods and (semi-)implicit time stepping schemes for phase field models. Based on extensive research experience in these areas and strong computing and software developing capabilities of the supporting institution, we plan to study elastic strain energy and saddle point problem for phase field model exploiting adaptive method and highly efficient (semi-)implicit time stepping schemes. Our research has the following features: it is aimed at the state-of-the-art algorithms and the frontier problems of phase field model; The design and analysis of the algorithms is guided by the balance between the model error and the

英文关键词： phase field；transition state；adaptive；large time step；extreme-scale parallel