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

光谱方法已被证明是有效的近似高梯度带出现在失效过程中。这些方法在固体力学中是有效的，当应用于小块或区域时，这些小块或区域对应于高梯度区域，如剪切带，再加上问题的其余部分的有限元离散化。在这里，将开发自适应程序，从溶液的性质（例如应变场）确定这些谱域的位置和范围。这些数值方法将在大规模计算中用于研究剪切带的结构及其生长的影响因素。光谱斑块或子域的使用提供了高梯度波段的高分辨率。子域和补丁之间的映射将被用来自适应地增强分辨率。由于使用了子域，这些方法自然适合于MIMD并行计算机。为利用这种并行性而设计的实现将被开发出来。这些方法将在与材料成形过程有关的大规模计算研究中实施和应用。特别地，不完美和热耦合在剪切带发展中的作用将被研究。此外，这些方法将应用于具有多级反应机制的气体燃烧动力学的计算研究。

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.