Abstract In this paper, we propose and evaluate fast, scalable approaches for solving the linear complementarity problems (LCP) arising from the fluid pressure equations with separating solid boundary conditions. Specifically, we present a policy iteration method, a penalty method, and a modified multigrid method, and demonstrate that each is able to properly handle the desired boundary conditions. Moreover, we compare our proposed methods against existing approaches and show that our solvers are more efficient and exhibit better scaling behavior; that is, the number of iterations required for convergence is essentially independent of grid resolution, and thus they are faster at larger grid resolutions. For example, on a 2563 grid our multigrid method was 30 times faster than the prior multigrid method in the literature.

We propose an approach for computing mutual information in rigid multimodality image registration. Images to be registered are modeled as functions defined on a continuous image domain. Analytic forms of the probability density functions for the images and the joint probability density function are first defined in 1D. We describe how the entropies of the images, the joint entropy, and mutual information can be computed accurately by a numerical method. We then extend the method to 2D and 3D. The mutual information function generated is smooth and does not seem to have the typical interpolation artifacts that are commonly observed in other standard models. The relationship between the proposed method and the partial volume (PV) model is described. In addition, we give a theoretical analysis to explain the nonsmoothness of the mutual information function computed by the PV model. Numerical experiments in 2D and 3D are presented to illustrate the smoothness of the mutual information function, which leads to robust and accurate numerical convergence results for solving the image registration problem.

Simulating natural phenomena has always been a focal point for computer graphics research. Its importance goes beyond the production of appealing presentations, since research in this area can contribute to the scientific understanding of complex natural processes. The natural phenomena, known as the Aurora Borealis and Aurora Australis, are geomagnetic phenomena of impressive visual characteristics and remarkable scientific interest. Aurorae present a complex behavior that arises from interactions between plasma (hot, ionized gases composed of ions, electrons, and neutral atoms) and Earth's electromagnetic fields. Previous work on the visual simulation of auroral phenomena have focused on static physical models of their shape, modeled from primitives, like sine waves. In this article, we focus on the dynamic behavior of the aurora, and we present a physically-based model to perform 3D visual simulations. The model takes into account the physical parameters and processes directly associated with plasma flow, and can be extended to simulate the dynamics of other plasma phenomena as well as astrophysical phenomena. The partial differential equations associated with these processes are solved using a complete multigrid implementation of the electromagnetic interactions, leading to a simulation of the shape and motion of the auroral displays. In order to illustrate the applicability of our model, we provide simulation sequences rendered using a distributed forward mapping approach.

Abstract A mathematical model is presented to simulate the growth of a plant leaf. The tissue in the leaf has been regarded as a viscous, incompressible fluid whose 2D expansion comes from the non‐zero specific growth rate in area. The resulting system of equations are composed of the modified Navier‐Stokes equations. The level set method is used to capture the expanding leaf front. Numerical simulations indicate that different portions of the leaf expand at different rates, which is consistent with the biological observations in the growth of a plant leaf. Numerical results for the case of the Xanthium leaf growth are also presented. A standard ray tracing technique is applied to produce an animation simulating the leaf growth process of three days. The key results with their physical and practical implications are discussed. Copyright © 2004 John Wiley & Sons, Ltd.