Modeling and simulation by multiple scale meshfree methods

We have established computational methodologies which include both the particle characteristics and multiscale analysis of the meshfree method. By incorporating these methodologies in a single algorithm, new possibilities for advancing the science of simulation arise. For example, in failure of materials, the process starts with damage at very small scales, which interact to form damage at mesoscales and finally macroscopic fracture. The numerical results of multiple-scale RKPM show a strong potential for capturing the physical phenomena such as shear band, large deformation, and the material instability during damage evolution. Another unique feature of meshfree methods which has recently emerged is their capability to encompass multi-scale analysis. This feature arises from the relationship between meshfree methods and wavelets and it enables phenomena characterized by significantly different length scales to be solved more effectively than conventional methods. By exploiting some of the recently discovered properties of wavelets as well as new wavelets developed specifically for these purposes, it is possible to effectively attack problems where critical phenomena take place at different scales. These methods are also promising in problems such as computational fluid dynamics and large eddy simulations of turbulence.