We present a novel algorithm to solve dense linear systems using graphics processors (GPUs). We reduce matrix decomposition and row operations to a series of rasterization problems on the GPU. These include new techniques for streaming index pairs, swapping rows and columns and parallelizing the computation to utilize multiple vertex and fragment processors. We also use appropriate data representations to match the rasterization order and cache technology of graphics processors. We have implemented our algorithm on different GPUs and compared the performance with optimized CPU implementations. In particular, our implementation on a NVIDIA GeForce 7800 GPU outperforms a CPU-based ATLAS implementation. Moreover, our results show that our algorithm is cache and bandwidth efficient and scales well with the number of fragment processors within the GPU and the core GPU clock rate. We use our algorithm for fluid flow simulation and demonstrate that the commodity GPU is a useful co-processor for many scientific applications.

Figure 1: Adaptive dynamics of articulated characters. In this complex scene, 200 human characters, represented by 17, 800 rigid bodies and 19, 000 degrees of freedom, are suddenly pushed away from the camera due to applied forces. Our adaptive dynamics algorithm allows an animator to progressively reduce the number of simulated joints in the characters as their distance to the camera increases, while automatically determining which joints should be animated to best approximate the characters motion. Depending on the total amount of simplification specified by the animator, a potentially significant speed-up can be achieved over typical linear-time forward dynamics algorithms.Abstract: Forward dynamics is central to physically-based simulation and control of articulated bodies. We present an adaptive algorithm for computing forward dynamics of articulated bodies: using novel motion error metrics, our algorithm can automatically simplify the dynamics of a multi-body system, based on the desired number of degrees of freedom and the location of external forces and active joint forces. We demonstrate this method in plausible animation of articulated bodies, including a large-scale simulation of 200 animated humanoids and multi-body dynamics systems with many degrees of freedom. The graceful simplification allows us to achieve up to two orders of magnitude performance improvement in several complex benchmarks.

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Fast contact handling of soft articulated characters is a computationally challenging problem, in part due to complex interplay between skeletal and surface deformation. We present a fast, novel algorithm based on a layered representation for articulated bodies that enables physically-plausible simulation of animated characters with a high-resolution deformable skin in real time. Our algorithm gracefully captures the dynamic skeleton-skin interplay through a novel formulation of elastic deformation in the pose space of the skinned surface. The algorithm also overcomes the computational challenges by robustly decoupling skeleton and skin computations using careful approximations of Schur complements, and efficiently performing collision queries by exploiting the layered representation. With this approach, we can simultaneously handle large contact areas, produce rich surface deformations, and capture the collision response of a character's skeleton.