Related papers: Position-Based Nonlinear Gauss-Seidel for Quasista…
The peridynamic theory brings advantages in dealing with discontinuities, dynamic loading, and non-locality. The integro-differential formulation of peridynamics poses challenges to numerical solutions of complicated and practical problems.…
This paper proposes a predefined-time (PDT) neurodynamic approach with time-varying coefficients for solving mixed variational inequality problems (MVIs). A class of first-order proximal neurodynamic models is developed to guarantee…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
Many tasks in robot-assisted surgery require planning and controlling manipulators' motions that interact with highly deformable objects. This study proposes a realistic, time-bounded simulator based on Position-based Dynamics (PBD)…
In this paper, we introduce a novel bond-based peridynamic model that utilizes a Gaussian kernel function. Previous peridynamic models, when directly discretized, have exhibited a lack of asymptotically compatibility with their…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
To stabilize PDE models, control laws require space-dependent functional gains mapped by nonlinear operators from the PDE functional coefficients. When a PDE is nonlinear and its "pseudo-coefficient" functions are state-dependent, a…
We present a new method for real-time physics-based simulation supporting many different types of hyperelastic materials. Previous methods such as Position Based or Projective Dynamics are fast, but support only limited selection of…
Probabilistic collision detection (PCD) is essential in motion planning for robots operating in unstructured environments, where considering sensing uncertainty helps prevent damage. Existing PCD methods mainly used simplified geometric…
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…
In this work we develop the Spectral Ewald Accelerated Stokesian Dynamics (SEASD), a novel computational method for dynamic simulations of polydisperse colloidal suspensions with full hydrodynamic interactions. SEASD is based on the…
This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications.…
We develop and analyze an optimization-based method for the coupling of a static peri-dynamic (PD) model and a static classical elasticity model. The approach formulates the coupling as a control problem in which the states are the…
A nonlinear dynamical system model that approximates a microscopic Gibbs field model for the yielding of a viscoplastic material subjected to varying external stress recently reported in [1] is presented. The predictions of the model are in…
The high-index saddle dynamics (HiSD) method [J. Yin, L. Zhang, and P. Zhang, {\it SIAM J. Sci. Comput., }41 (2019), pp.A3576-A3595] serves as an efficient tool for computing index-$k$ saddle points and constructing solution landscapes.…
The companion paper "Higher-order in time quasi-unconditionally stable ADI solvers for the compressible Navier-Stokes equations in 2D and 3D curvilinear domains", which is referred to as Part I in what follows, introduces ADI (Alternating…
The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…
Grain boundary (GB) energy is a fundamental property that affects the form of grain boundary and plays an important role to unveil the behavior of polycrystalline materials. With a better understanding of grain boundary energy distribution…
Simulating stiff materials in applications where deformations are either not significant or can safely be ignored is a pivotal task across fields. Rigid body modeling has thus long remained a fundamental tool and is, by far, the most…
The choice of numerical integrator in approximating solutions to dynamic partial differential equations depends on the smallest time-scale of the problem at hand. Large-scale deformations in elastic solids contain both shear waves and bulk…