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We present a generalized algorithm based on a spherical harmonics expansion method for efficient computation of the three-dimensional gravitational potential on a multi-patch grid in spherical geometry. Instead of solving for the…
On a global level, ecological communities are being perturbed at an unprecedented rate by human activities and environmental instabilities. Yet, we understand little about what factors facilitate or impede long-term persistence of these…
In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several…
In the transformative landscape of smart cities, the integration of the cutting-edge web technologies into time series forecasting presents a pivotal opportunity to enhance urban planning, sustainability, and economic growth. The…
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns…
The multiscale patch scheme is built from given small micro-scale simulations of complicated physical processes to empower large macro-scale simulations. By coupling small patches of simulations over unsimulated spatial gaps, large savings…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
We consider one dimensional lattice diffusion model on a microscale grid with many discrete diffusivity values which repeat periodicially. Computer algebra explores how the dynamics of small coupled `patches' predict the slow emergent…
With the increasing number of components and further miniaturization the mean time between faults in supercomputers will decrease. System level fault tolerance techniques are expensive and cost energy, since they are often based on…
This is the first paper in a series aimed to implement boundary conditions consistent with the constraints' propagation in 3D numerical relativity. Here we consider spherically symmetric black hole spacetimes in vacuum or with a minimally…
Tensor-network simulations of quantum many-body dynamics are fundamentally limited by entanglement build-up, which leads to exponentially growing computational costs. Furthermore, these classical simulation algorithms are inherently…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
The exact propagators of two one-dimensional systems with time-dependent external fields are presented by following the path-integral method. It is shown that the Bloch acceleration theorem can be generalized to the impulse-momentum theorem…
In this paper, we investigate the global exponential stability for complex-valued recurrent neural networks with asynchronous time delays by decomposing complex-valued networks to real and imaginary parts and construct an equivalent…
Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…
The numerical simulation of two-dimensional quantum many-body systems away from equilibrium constitutes a major challenge for all known computational methods. We investigate the utility of Tree Tensor Network (TTN) states to solve the…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
We describe in this article a new code for evolving axisymmetric isolated systems in general relativity. Such systems are described by asymptotically flat space-times which have the property that they admit a conformal extension. We are…