Related papers: A Jacobian-free Newton-Krylov method for cell-cent…
In this thesis we study the preconditioning of square, non-symmetric and real Toeplitz systems. We prove theoretical results, which constitute sufficient conditions for the efficiency of the proposed preconditioners and the fast convergence…
This paper is concerned with numerical analysis of two fully discrete Chorin-type projection methods for the stochastic Stokes equations with general non-solenoidal multiplicative noise. The first scheme is the standard Chorin scheme and…
In parallel simulation, convergence and parallelism are often seen as inherently conflicting objectives. Improved parallelism typically entails lighter local computation and weaker coupling, which unavoidably slow the global convergence.…
We present a specific-purpose globalized and preconditioned Newton-CG solver to minimize a metric-aware curved high-order mesh distortion. The solver is specially devised to optimize curved high-order meshes for high polynomial degrees with…
For several classes of mathematical models that yield linear systems, the splitting of the matrix into its Hermitian and skew Hermitian parts is naturally related to properties of the underlying model. This is particularly so for…
In this paper we present a new approach for dynamic motion planning for legged robots. We formulate a trajectory optimization problem based on a compact form of the robot dynamics. Such a form is obtained by projecting the rigid body…
This paper analyzes block-coordinate proximal gradient methods for minimizing the sum of a separable smooth function and a (nonseparable) nonsmooth function, both of which are allowed to be nonconvex. The main tool in our analysis is the…
The use of block Krylov subspace methods for computing the solution to a sequence of shifted linear systems using subspace recycling was first proposed in [Soodhalter, SISC 2016], where a recycled shifted block GMRES algorithm (rsbGMRES)…
The paper studies a time-nonlocal multiphysics finite element method with Crank-Nicolson scheme for poroelasticity model with secondary consolidation. For the case where the physical parameters $\lambda,\lambda^*$ and $c_0$ are all finite…
The accuracy and stability of implicit CFD codes are frequently impaired by the decoupling between variables, which can ultimately lead to numerical divergence. Coupled solvers, which solve all the governing equations simultaneously, have…
Many practical imaging systems suffer from uncertainty in acquisition geometry -- such as projection angles in computed tomography or sensor positions in photoacoustic tomography -- leading to nonlinear inverse problems that require joint…
To meet the demand for complex geometries and high resolutions of small-scale flow structures, a two-stage fourth-order subcell finite volume (SCFV) method combining the gas-kinetic solver (GKS) with subcell techniques for compressible…
In this work, we present a framework for the matrix-free solution to a monolithic quasi-static phase-field fracture model with geometric multigrid methods. Using a standard matrix based approach within the Finite Element Method requires…
This paper makes the first attempt to apply newly developed upwind GFDM for the meshless solution of two-phase porous flow equations. In the presented method, node cloud is used to flexibly discretize the computational domain, instead of…
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…
Power flow calculations for systems with a large number of buses, e.g. grids with multiple voltage levels, or time series based calculations result in a high computational effort. A common power flow solver for the efficient analysis of…
We develop a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the…
A new Jacobian approximation is developed for use in quasi-Newton methods for solving systems of nonlinear equations. The new hypersecant Jacobian approximation is intended for the special case where the evaluation of the functions whose…
We present a simple and efficient variational finite difference method for simulating time-dependent Stokes flow in the presence of irregular free surfaces and moving solid boundaries. The method uses an embedded boundary approach on…
Fluid-structure interactions are central to many bio-molecular processes, and they impose a great challenge for computational and modeling methods. In this paper, we consider the immersed boundary method (IBM) for biofluid systems, and to…