Related papers: A variational quantum algorithm-based numerical me…
A parallel implementation of the Balancing Domain Decomposition by Constraints (BDDC) method is described. It is based on formulation of BDDC with global matrices without explicit coarse problem. The implementation is based on the MUMPS…
In this paper, a framework is proposed to simplify solving the infinite horizon average cost problem for the weakly coupled multi-dimensional systems. Specifically, to address the computational complexity issue, we first introduce a virtual…
An accelerated boundary integral method for Stokes flow of a suspension of deformable particles is presented for an arbitrary domain and implemented for the important case of a planar slit geometry. The computational complexity of the…
Modern Cloud/Edge architectures need to orchestrate multiple layers of heterogeneous computing nodes, including pervasive sensors/actuators, distributed Edge/Fog nodes, centralized data centers and quantum devices. The optimal assignment…
We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by multiply connected domains, nonconvex obstacles, and the calculation of force…
For solving the Poisson equation it is usually possible to discretize it into solving the corresponding linear system $Ax=b$.Variational quantum algorithms (VQAs) for the discreted Poisson equation have been studied before. We give a VQA…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…
An efficient, accurate, and flexible numerical method is proposed for the solution of the swimming problem of one or more autophoretic particles in the purely-diffusive limit. The method relies on successive boundary element solutions of…
We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical…
Viscous contact problems describe the time evolution of fluid flows in contact with a surface from which they can detach and reattach. These problems are of particular importance in glaciology, where they arise in the study of grounding…
We present a paradigm for developing arbitrarily high order, linear, unconditionally energy stable numerical algorithms for gradient flow models. We apply the energy quadratization (EQ) technique to reformulate the general gradient flow…
A framework is developed for a robust and highly accurate numerical solution of the coupled Stokes-Darcy system in three dimensions. The domain decomposition method is based on a Dirichlet-Neumann type splitting of the interface conditions…
In numerical approaches to solving differential equations on a lattice, a representation of the derivative operator that correctly matches the continuum behaviour of functions of momentum up to the band limit must be non-local. We present…
Recursive Marginal Quantization (RMQ) allows fast approximation of solutions to stochastic differential equations in one-dimension. When applied to two factor models, RMQ is inefficient due to the fact that the optimization problem is…
The accurate numerical simulation of turbulent incompressible flows is a challenging topic in computational fluid dynamics. For discretisation methods to be robust in the under-resolved regime, mass conservation as well as energy stability…
We present a framework wherein the trajectory optimization problem (or a problem involving calculus of variations) is formulated as a search problem in a discrete space. A distinctive feature of our work is the treatment of discretization…
In this study, we propose a new method for constrained combinatorial optimization using variational quantum circuits. Quantum computers are considered to have the potential to solve large combinatorial optimization problems faster than…
We propose a new discretization method for the Stokes equations. The method is an improved version of the method recently presented in [C. Lehrenfeld, J. Sch\"oberl, Comp. Meth. Appl. Mech. Eng., 361 (2016)] which is based on an…
The variational principle serves as a fundamental framework for describing equilibrium states of physical systems via the minimization or extremization of an energy-like functional. While quantum algorithms have demonstrated promising…
Quantum computers promise a great computational advantage over classical computers, yet currently available quantum devices have only a limited amount of qubits and a high level of noise, limiting the size of problems that can be solved…