Adaptive Multi-Domain Spectral Methods Applied to High Gradient Problems in Solid Mechanics

谱方法已被证明是有效的近似 失效过程中出现的高梯度带。 这些方法在固体力学中的应用是有效的， 对应于高梯度的小斑块或区域 区域，如剪切带，与有限元耦合 问题的其余部分的离散化。 在这里，自适应 将制定程序，以确定 这些谱域的解的性质，为 例如应变场。 将采用这些数值方法 在大规模计算中， 影响其成长的因素。 使用频谱补丁或子域提供了高度的 高梯度带的分辨率。 内部的映射 子域和补丁将被用来自适应地增强 分辨率 这些方法，因为他们的就业， 子域，自然适合MIMD并行计算机。 旨在利用这种并行性的实现将 开发 这些方法将得到大规模的实施和应用 与材料成形过程有关的计算研究。 在 特别是缺陷和热耦合的作用 研究剪切带的发展。 此外，这些 方法将应用于动力学的计算研究 具有多级反应机理的气体燃烧。

Spectral methods have been shown to be effective in approximating the high gradient bands which occur during failure processes. These methods are effective in solid mechanics when applied in small patches or domains, which correspond to the high gradient regions such as shear bands, coupled with a finite element discretization of the rest of the problem. Here, adaptive procedures will be developed to determine the location and extent of these spectral domains from properties of the solution, for example the strain field. These numerical methods will be employed in large scale computations to study the structure of shear bands and factors influencing their growth. The use of spectral patches or subdomains provides a high degree of resolution of high gradient bands. Mappings within the subdomains and patches will be employed to adaptively enhance the resolution. These methods, because of their employment of subdomains, lend themselves naturally to MIMD parallel computers. Implementations designed to exploit this parallelism, will be developed. These methods will be implemented and applied in large scale computational studies relating to materials forming processes. In particular the role of imperfections and thermal coupling in the development of shear bands will be studied. Additionally, these methods will be applied in computational studies of the dynamics of gaseous combustion with multiple stage reaction mechanisms.