Fig. 1. Our implicit solver simultaneously resolves cloth elasticity, non-penetration and exact Coulomb friction constraints at every body-cloth and cloth-cloth contact, largely improving physical realism over previous methods. This new solver especially allows us to simulate accurately the effect of a varying friction coefficient µ, capturing a diversity of cloth sliding motions and folding patterns as shown in this batwing dress example (from left to right, µ = 0, µ = 0.1, µ = 0.3, and µ = 0.6). In this example featuring 2,600 contact points on average, our solver converges at each time step (dt = 2ms) to a high precision in a few hundred milliseconds only.Cloth dynamics plays an important role in the visual appearance of moving characters. Properly accounting for contact and friction is of utmost importance to avoid cloth-body and cloth-cloth penetration and to capture typical folding and stick-slip behavior due to dry friction. We present here the first method able to account for cloth contact with exact Coulomb friction, treating both cloth self-contacts and contacts occurring between the cloth and an underlying character. Our key contribution is to observe that for a nodal system like cloth, the frictional contact problem may be formulated based on velocities as primary variables, without having to compute the costly Delassus operator. Then, by reversing the roles classically played by the velocities and the contact impulses, conical complementarity solvers of the literature can be adapted to solve for compatible velocities at nodes. To handle the full complexity of cloth dynamics scenarios, we have extended this base algorithm in two ways: first, towards the accurate treatment of frictional contact at any location of the cloth, through an adaptive node refinement strategy; second, towards the handling of multiple constraints at each node, through the duplication of constrained nodes and the adding of pin constraints between duplicata. Our method allows us to handle the complex cloth-cloth and cloth-body interactions in full-size garments with an unprecedented level of realism compared to former methods, while maintaining reasonable computational timings.

A transient spherical multipole expansion-like solution for acoustic scattering from a spherical object is derived within a mesh-free and singularity-free time domain integral equation (TDIE) framework for the sound-soft, sound-rigid and penetrable cases. The method is based on an expansion of the time domain Green's function that allows independent evaluation of spatial and temporal convolutions. The TDIE system is solved by descretizing the integral equations in space and time, forming a matrix system via the method of moments, and solving the system with the marching on in time algorithm. Spatial discretization using tesseral harmonics leads to closed form expressions for spatial integrals, and use of a strictly band limited temporal interpolant permits efficient, accurate computation of temporal convolutions via numerical quadrature. The accuracy of these integrations ensures late time stability and accuracy of the deconvolution data. Results presented demonstrate the accuracy and convergence of the approach for broadband simulations compared with Fourier transformed analytical data.

The analysis of electromagnetic scattering has long been performed on a discrete representation of the geometry. This representation is typically continuous but not differentiable. The need to define physical quantities on this geometric representation has led to development of sets of basis functions that need to satisfy constraints at the boundaries of the elements/tesselations (viz., continuity of normal or tangential components across element boundaries). For electromagnetics, these result in either curl/div-conforming basis sets. The geometric representation used for analysis is in stark contrast with that used for design, wherein the surface representation is higher order differentiable. Using this representation for both geometry and physics on geometry has several advantages, and is eludicated in Hughes et al., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering 194 (39-41) (2005). Until now, a bulk of the literature on isogeometric methods have been limited to solid mechanics, with some effort to create NURBS based basis functions for electromagnetic analysis. In this paper, we present the first complete isogeometry solution methodology for the electric field integral equation as applied to simply connected structures. This paper systematically proceeds through surface representation using subdivision, definition of vector basis functions on this surface, to fidelity in the solution of integral equations. We also present techniques to stabilize the solution at low frequencies, and impose a Calderón preconditioner. Several results presented serve to validate the proposed approach as well as demonstrate some of its capabilities.

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