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We present an efficient numerical method, inspired by transformation optics, for solving the Poisson equation in complex and arbitrarily shaped geometries. The approach operates by mapping the physical domain to a uniform computational…
We consider the problem of coarse-graining in the context of finite-volume fluid models. If a variable is defined on a high-resolution grid it may be coarse-grained so that it is defined on a grid of lower resolution. In general this will…
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…
Abstract Simulation domain in field-aligned coordinates of the electrostatic gyrokinetic nonlinear turbulence global code, NLT, is extended to include the magnetic axis. The artificial boundary near the magnetic axis is replaced by the…
Cartesian-grid methods with Adaptive Mesh Refinement (AMR) are ideally suited for simulating the breaking of waves, the formation of spray, and the entrainment of air around ships. As a result of the cartesian-grid formulation, minimal…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
Immersed boundary methods are extensively used for simulations of dynamic solid objects interacting with fluids due to their computational efficiency and modelling flexibility compared to body-fitted grid methods. However, thin geometries,…
The objective of this paper is to derive the essential invariance and contraction properties for the geometric periodic systems, which can be formulated as a category of differential inclusions, and primarily rendered in the phase…
The artificial viscosity approach for curing the carbuncle phenomenon (a numerical problem, also known as the shock instability) in shock-capturing methods has been recently presented and successfully tested on the first-order schemes in…
Engineering simulations using boundary-value partial differential equations often implicitly assume that the uncertainty in the location of the boundary has a negligible impact on the output of the simulation. In this work, we develop a…
In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques…
In this paper, mathematical models for cuff-tissue-artery system are developed and simplified into an axisymmetric problem in space. It is nonlinear properties of cuff and artery wall that make it difficult to solve elastic equations…
In this work, we utilize discrete geometric mechanics to derive a 2nd-order variational integrator so as to simulate rigid body dynamics. The developed integrator is to simulate the motion of a free rigid body and a quad-rotor. We…
We develop a curvilinear invariant set of the diffusion tensor which may be applied to Diffusion Tensor Imaging measurements on tissues and porous media. This new set is an alternative to the more common invariants such as fractional…
Cohesive granular materials such as wet sand, snow, and powders can flow like a viscous liquid. However, the elementary mechanisms of momentum transport in such athermal particulate fluids are elusive. As a result, existing models for…
We describe a grid-based numerical method for 3D hydrodynamic cosmological simulations which is adaptive in space and time and combines the best features of higher order--accurate Godunov schemes for Eulerian hydrodynamics with adaptive…
Certain wheeled mobile robots e.g., electric wheelchairs, can operate through indirect joystick controls from users. Correct steering angle becomes essential when the user should determine the vehicle direction and velocity, in particular…
A variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of spacetime based on infalling geodesics,…
Recent studies have shown that many nonconvex machine learning problems satisfy a generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms are not fully adapted to such…
Grasping deformable objects is not well researched due to the complexity in modelling and simulating the dynamic behavior of such objects. However, with the rapid development of physics-based simulators that support soft bodies, the…