Lattice deformers are a popular option for modeling the behavior of elastic bodies as they avoid the need for conforming mesh generation, and their regular structure offers significant opportunities for performance optimizations. Our work expands the scope of current lattice-based elastic deformers, adding support for a number of important simulation features. We accommodate complex nonlinear, optionally anisotropic materials while using an economical one-point quadrature scheme. Our formulation fully accommodates near-incompressibility by enforcing accurate nonlinear constraints, supports implicit integration for large time steps, and is not susceptible to locking or poor conditioning of the discrete equations. Additionally, we increase the accuracy of our solver by employing a novel high-order quadrature scheme on lattice cells overlapping with the model boundary, which are treated at sub-cell precision. Finally, we detail how this accurate boundary treatment can be implemented at a minimal computational premium over the cost of a voxel-accurate discretization. We demonstrate our method in the simulation of complex musculoskeletal human models.

M., Sifakis, E. 2016. A scalable Schur-complement fl uids solver for heterogeneous compute platforms.Figure 1: Left: Smoke injected into a model of the bronchi. Color illustrates vorticity magnitude. Simulation contains 1.8 billion active cells, sparsely occupying a 8192 2 ×4096 background grid. Right: Smoke injected from the bottom of a cylinder, and forced through a metal gasket (rendered semi-transparent) with a twisted bundle of cylindrical holes. Total of 1.2 billion active cells, in a 1024 2 ×2048 background grid. AbstractWe present a scalable parallel solver for the pressure Poisson equation in fluids simulation which can accommodate complex irregular domains in the order of a billion degrees of freedom, using a single server or workstation fitted with GPU or Many-Core accelerators. The design of our numerical technique is attuned to the subtleties of heterogeneous computing, and allows us to benefit from the high memory and compute bandwidth of GPU accelerators even for problems that are too large to fit entirely on GPU memory. This is achieved via algebraic formulations that adequately increase the density of the GPU-hosted computation as to hide the overhead of offloading from the CPU, in exchange for accelerated convergence. Our solver follows the principles of Domain Decomposition techniques, and is based on the Schur complement method for elliptic partial differential equations. A large uniform grid is partitioned in non-overlapping subdomains, and bandwidth-optimized (GPU or Many-Core) accelerator cards are used to efficiently and concurrently solve independent Poisson problems on each resulting subdomain. Our novel contributions are centered on the careful steps necessary to assemble an accurate global solver from these constituent blocks, while avoiding excessive communication or dense linear algebra. We ultimately produce a highly effective Conjugate Gradients preconditioner, and demonstrate scalable and accurate performance on high-resolution simulations of water and smoke flow.

A preliminary skin flap simulator has been demonstrated to be an effective teaching platform for the real-time elucidation of local flap principles. Future work will involve adaptation of the system to facial flaps, breast surgery, cleft lip, and other problems in plastic surgery as well as surgery in general.