MULTIRESOLUTION REPRODUCING KERNEL PARTICLE METHODS

Reproducing Kernel Particle Methods (RKPM) with a built-in feature of multiresolution analysis are addressed. Some fundamental concepts such as reproducing conditions, and correction function are constructed to systematize the framework of RKPM. In particular, Fourier analysis, a s a tool, is exploited to further elaborate RKPM in the frequency doma in. Furthermore, we address error estimation and convergence propertie s. We present several applications which confirm the widespread applic ability of multiresolution RKPM.