Related papers: Essentially Non-oscillatory Spectral Volume Method…
We present a finite volume method that is applicable to hyperbolic PDEs including spatially varying and semilinear nonconservative systems. The spatial discretization, like that of the well-known Clawpack software, is based on solving…
Linear approximation approaches suffer from Gibbs oscillations when approximating functions with singularities. ENO-SR resolution is a local approach avoiding oscillations and with a full order of accuracy, but a loss of regularity of the…
In this study, a new framework of constructing very high order discontinuity-capturing schemes is proposed for finite volume method. These schemes, so-called $\mathrm{P}_{n}\mathrm{T}_{m}-\mathrm{BVD}$ (polynomial of $n$-degree and THINC…
Single particle cryo-electron microscopy has become a critical tool in structural biology over the last decade, able to achieve atomic scale resolution in three dimensional models from hundreds of thousands of (noisy) two-dimensional…
Classical phase retrieval problem is the recovery of a constrained image from the magnitude of its Fourier transform. Although there are several well-known phase retrieval algorithms including the hybrid input-output (HIO) method, the…
We present a new version of conservative ADER-WENO finite volume schemes, in which both the high order spatial reconstruction as well as the time evolution of the reconstruction polynomials in the local space-time predictor stage are…
A series of third- and fifth-order hybrid compact least-squares central weighted essentially non-oscillatory schemes are proposed and applied to curvilinear structured grids for the finite volume method. In smooth regions, compact…
Spectral residual methods are derivative-free and low-cost per iteration procedures for solving nonlinear systems of equations. They are generally coupled with a nonmonotone linesearch strategy and compare well with Newton-based methods for…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
We present the optimal design of a spectral method widely used to initialize nonconvex optimization algorithms for solving phase retrieval and other signal recovery problems. Our work leverages recent results that provide an exact…
We present a class of high order finite volume schemes for the solution of non-conservative hyperbolic systems that combines the one-step ADER-WENO finite volume approach with space-time adaptive mesh refinement (AMR). The resulting…
In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced…
In this paper, a high-order moment-based multi-resolution Hermite weighted essentially non-oscillatory (HWENO) scheme is designed for hyperbolic conservation laws. The main idea of this scheme is derived from our previous work [J. Comput.…
We illustrate that numerical solutions of high order finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme for some nonconvex conservation laws perform poorly or converge to the entropy solution in a slow speed. The…
Learning the structure of a network from time series data, in particular cyclostationary data, is of significant interest in many disciplines such as power grids, biology and finance. In this article, an algorithm is presented for…
A novel hybrid spectral difference/embedded finite volume method is introduced in order to apply a discontinuous high-order method for large scale engineering applications involving discontinuities in the flows with complex geometries. In…
There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…
A high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions is presented. A high order one-step time discretization is achieved using a local space-time discontinuous Galerkin…
Determining the three-dimensional structure of proteins and protein complexes at atomic resolution is a fundamental task in structural biology. Over the last decade, remarkable progress has been made using "single particle" cryo-electron…
To solve large-scale or high-resolution topology optimization problem, a novel algorithm is developed based on modified bi-directional evolutionary structure optimization (BESO) and extended finite element method (XFEM). Within XFEM, a set…