Implementation and analysis of adaptive algorithms for the numerical solution of partial differential equations

偏微分方程数值求解自适应算法的实现与分析

• 批准号: 311796-2008
• 负责人: Haynes, Ronald
• 金额: $ 0.39万
• 依托单位: Memorial University of Newfoundland
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2009
• 资助国家: 加拿大
• 起止时间: 2009-01-01 至 2010-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=427878
• 关键词: Implementation; analysis; adaptive; algorithms; numerical

Mathematically, many models of interesting physical phenomena are written as partial differential equations (PDEs). Except for certain idealized situations, the PDEs which result are not amenable to analytical solution. Instead we rely on numerical approximations. I am particularly interested in time-dependent PDEs in two or three spatial dimensions whose solutions exhibit large solution variation, some type of singularity, blow-up or moving fronts. To efficiently track these regions of interest it is necessary to develop methods which adapt to the rapidly evolving features of the solution.

在数学上，许多有趣的物理现象的模型被写成偏微分方程（PDE）。除了某些理想化的情况，所得到的偏微分方程不适合于解析解。 相反，我们依赖于数值近似。 我特别感兴趣的时间依赖的偏微分方程在两个或三个空间维度，其解决方案表现出大的解决方案的变化，某种类型的奇异性，爆破或移动前沿。为了有效地跟踪这些感兴趣的区域，有必要开发适应解决方案的快速演变特征的方法。