48 citations · 237 across the 48 of their papers we have counts for
19 papers · 1 filter
Slip optimization on arbitrary 3D microswimmers: a reduced-dimension and boundary-integral framework
Marc Bonnet, Kausik Das, Shravan Veerapaneni +1
This article presents a computational framework for determining the optimal slip velocity of a microswimmer with arbitrary three-dimensional geometry suspended in a viscous fluid.…
Space-time adaptive methods for parabolic evolution equations
Jun Wang, Jie Su, Leslie Greengard +2
We present a family of integral equation-based solvers for the heat equation, reaction-diffusion systems, the unsteady Stokes equation and the incompressible Navier-Stokes equation…
A convergent finite element method for two-phase Stokes flow driven by surface tension
Genming Bai, Harald Garcke, Shravan Veerapaneni
We present the first convergence proof for an iso-parametric finite element discretization of two-phase Stokes flow in , , with interface dynamics gov…
Convergence analysis for the Barrett--Garcke--Nurnberg method of transport type for evolving curves
Genming Bai, Harald Garcke, Shravan Veerapaneni
In this paper, we propose a Barrett-Garcke-Nurnberg (BGN) method for evolving geometries under general flows and present the corresponding convergence analysis. Specifically, we ex…
Quantum-inspired nonlinear Galerkin ansatz for high-dimensional HJB equations
Chuhao Sun, Asaf Cohen, James Stokes +1
Neural networks are increasingly recognized as a powerful numerical solution technique for partial differential equations (PDEs) arising in diverse scientific computing domains, in…
An Incremental Tensor Train Decomposition Algorithm
Doruk Aksoy, David J. Gorsich, Shravan Veerapaneni +1
We present a new algorithm for incrementally updating the tensor train decomposition of a stream of tensor data. This new algorithm, called the {\em tensor train incremental core e…
Tensor-Train Compression of Discrete Element Method Simulation Data
Saibal De, Eduardo Corona, Paramsothy Jayakumar +1
We propose a framework for discrete scientific data compression based on the tensor-train (TT) decomposition. Our approach is tailored to handle unstructured output data from discr…
Quantum-inspired variational algorithms for partial differential equations: Application to financial derivative pricing
Tianchen Zhao, Chuhao Sun, Asaf Cohen +2
Variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of…
A fast, high-order scheme for evaluating volume potentials on complex 2D geometries via area-to-line integral conversion and domain mappings
Thomas G. Anderson, Hai Zhu, Shravan Veerapaneni
This article presents a new high-order accurate algorithm for finding a particular solution to a linear, constant-coefficient partial differential equation (PDE) by means of a conv…
A fast direct solver for integral equations on locally refined boundary discretizations and its application to multiphase flow simulations
Yabin Zhang, Adrianna Gillman, Shravan Veerapaneni
In transient simulations of particulate Stokes flow, to accurately capture the interaction between the constituent particles and the confining wall, the discretization of the wall…
High-order close evaluation of Laplace layer potentials: A differential geometric approach
Hai Zhu, Shravan Veerapaneni
This paper presents a new approach for solving the close evaluation problem in three dimensions, commonly encountered while solving linear elliptic partial differential equations v…
Fast integral equation methods for linear and semilinear heat equations in moving domains
Jun Wang, Leslie Greengard, Shidong Jiang +1
We present a family of integral equation-based solvers for the linear or semilinear heat equation in complicated moving (or stationary) geometries. This approach has significant ad…
Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme
Bowei Wu, Hai Zhu, Alex Barnett +1
We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The ke…
Tensor Train accelerated solvers for nonsmooth rigid body dynamics
Eduardo Corona, David Gorsich, Paramsothy Jayakumar +1
In the last two decades, increased need for high-fidelity simulations of the time evolution and propagation of forces in granular media has spurred renewed interest in discrete ele…
Boundary integral equation analysis for suspension of spheres in Stokes flow
Eduardo Corona, Shravan Veerapaneni
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…
A unified integral equation scheme for doubly-periodic Laplace and Stokes boundary value problems in two dimensions
Alex H. Barnett, Gary Marple, Shravan Veerapaneni +1
We present a spectrally-accurate scheme to turn a boundary integral formulation for an elliptic PDE on a single unit cell geometry into one for the fully periodic problem. Applicat…
An integral equation formulation for rigid bodies in Stokes flow in three dimensions
Eduardo Corona, Leslie Greengard, Manas Rachh +1
We present a new derivation of a boundary integral equation (BIE) for simulating the three-dimensional dynamics of arbitrarily-shaped rigid particles of genus zero immersed in a St…
A fast algorithm for simulating multiphase flows through periodic geometries of arbitrary shape
Gary Marple, Alex Barnett, Adrianna Gillman +1
This paper presents a new boundary integral equation (BIE) method for simulating particulate and multiphase flows through periodic channels of arbitrary smooth shape in two dimensi…
Spectrally-accurate quadratures for evaluation of layer potentials close to the boundary for the 2D Stokes and Laplace equations
Alex H. Barnett, Bowei Wu, Shravan K. Veerapaneni
Dense particulate flow simulations using integral equation methods demand accurate evaluation of Stokes layer potentials on arbitrarily close interfaces. In this paper, we generali…