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The fixed-stress splitting scheme is a popular method for iteratively solving the Biot equations. The method successively solves the flow and mechanic subproblems while adding a stabilizing term to the flow equation, which includes a…
In wave propagation problems, finite difference methods implemented on staggered grids are commonly used to avoid checkerboard patterns and to improve accuracy in the approximation of short-wavelength components of the solutions. In this…
We propose a novel belief space planning technique for continuous dynamics by viewing the belief system as a hybrid dynamical system with time-driven switching. Our approach is based on the perturbation theory of differential equations and…
Semidefinite programs (SDPs) are a framework for exact or approximate optimization that have widespread application in quantum information theory. We introduce a new method for using reductions to construct integrality gaps for SDPs. These…
Consistent splitting schemes are among the most accurate pressure segregation methods, incurring no splitting errors or spurious boundary conditions. Nevertheless, their theoretical properties are not yet fully understood, especially when…
Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation…
Mini-batch stochastic gradient descent (SGD) is state of the art in large scale distributed training. The scheme can reach a linear speedup with respect to the number of workers, but this is rarely seen in practice as the scheme often…
We present a novel technique for imposing non-linear entropy conservative and entropy stable wall boundary conditions for the resistive magnetohydrodynamic equations in the presence of an adiabatic wall or a wall with a prescribed heat…
In this article, we present entropy stable discontinuous Galerkin numerical schemes for equations of special relativistic hydrodynamics with the ideal equation of state. The numerical schemes use the summation by parts (SBP) property of…
We propose a stochastic approximation (SA) based method with randomization of samples for policy evaluation using the least squares temporal difference (LSTD) algorithm. Our proposed scheme is equivalent to running regular temporal…
In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD)…
In this paper, an improvement of the finite difference time domain (FDTD) method using a non-standard finite difference scheme is presented. The standard numerical scheme for the second derivative in the spatial domain is replaced by a…
The present paper proposes new fully discrete schemes for long-time approximations of stochastic partial differential equations (SPDEs) with non-globally Lipschitz coefficients in a bounded domain $D \subset \R^d, d =1,2,3 $. A novel family…
This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…
Position based dynamics is a powerful technique for simulating a variety of materials. Its primary strength is its robustness when run with limited computational budget. We develop a novel approach to address problems with PBD for…
This paper proposes an unconditionally stable numerical method for solving a nonlinear Sobolev model with distributed delay. The proposed computational approach approximates the time derivative by interpolation technique whereas the spatial…
Based on techniques by (S.J. Wright 1998) for finite-dimensional optimization, we investigate a stabilized sequential quadratic programming method for nonlinear optimization problems in infinite-dimensional Hilbert spaces. The method is…
We outline a partial-fractions decomposition method for determining the one-particle spectral function and single-particle density of states of a correlated electronic system on a finite lattice in the non self-consistent T-matrix…
In this work, we extend the Spatiotemporal Tube (STT) framework to address Probabilistic Temporal Reach-Avoid-Stay (PrT-RAS) tasks in dynamic environments with uncertain obstacles. We develop a real-time tube synthesis procedure that…
We develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm incorporates a variance reduction mechanism and the resulting…