The development of a parallel three-dimensional (3-D) adaptive mesh refinement (PAMR) scheme for an unstructured tetrahedral mesh using dynamic domain decomposition on a memory-distributed machine is presented in detail. A memory-saving cell-based data structure is designed such that the resulting mesh information can be readily utilized in both nodeor cell-based numerical methods. The general ...

The time-dependent Schrödinger equation describes quantum dynamical phenomena. Solving it numerically, the small-scale interactions that are modeled require very fine spatial resolution. At the same time, the solutions are localized and confined to small regions in space. Using the required resolution over the entire high-dimensional domain often makes the model problems intractable due to the ...

Subdivision schemes are iterative procedures to construct curves and constitute fundamental tools in Computer Aided Design. Starting with an initial control polygon, a subdivision scheme refines the computed values at the previous step according to some basic rules. The scheme is said to be convergent if there exists a limit curve. The computed values define a control polygon in each step. This...

Dendritic growth, and the formation of material microstructure in general, necessarily involves a wide range of length scales from the atomic up to sample dimensions. The phase field approach of Langer, enhanced by optimal asymptotic methods and adaptive mesh refinement, copes with this range of scales, and provides an effective way to move phase boundaries. However, it fails to preserve memory...

Simulating fluid flow at micro level is an ongoing problem. Simplified macroscopic flow models like Darcy’s law is unable to estimate fluid dynamic properties of porous media. The digital sample reconstruction by high resolution X-ray computed tomography scanning and fluid-dynamics simulation, together with the increasing power of super-computers, allow to carry out pore-scale simulations throu...

We consider a Fredholm integral equation of the second kind in L1([a, b],C), with a weakly singular kernel. Sufficient conditions are given for the existence and uniqueness of the solution. We adapt the product integration method proposed in C0([a, b],C) to apply it in L1([a, b],C), and discretize the equation. To improve the accuracy of the approximate solution, we use different iterative refi...