Related papers: Reconstruction of finite volume solution for param…
This paper derives a new class of adaptive regularization parameter choice strategies that can be effectively and efficiently applied when regularizing large-scale linear inverse problems by combining standard Tikhonov regularization and…
In this work a new finite element based Method of Relaxed Streamline Upwinding is proposed to solve hyperbolic conservation laws. Formulation of the proposed scheme is based on relaxation system which replaces hyperbolic conservation laws…
A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the…
We describe a novel Godunov-type numerical method for solving the equations of resistive relativistic magnetohydrodynamics. In the proposed approach, the spatial components of both magnetic and electric fields are located at zone interfaces…
A higher order Godunov method for the radiation subsystem of radiation hydrodynamics is presented. A key ingredient of the method is the direct coupling of stiff source term effects to the hyperbolic structure of the system of conservation…
We consider an inverse boundary value problem for a model time-harmonic equation of acoustic tomography of moving fluid with variable current velocity, sound speed, density and absorption. In the present article it is assumed that at fixed…
We describe an iterative method to optimize the multi-scale entanglement renormalization ansatz (MERA) for the low-energy subspace of local Hamiltonians on a D-dimensional lattice. For translation invariant systems the cost of this…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…
In this paper, we investigate the inverse problem on determining the spatial component of the source term in a hyperbolic equation with time-dependent principal part. Based on a newly established Carleman estimate for general hyperbolic…
We address numerical challenges in solving hyperbolic free boundary problems described by spherically symmetric conservation laws that arise in the modeling of tumor growth due to immune cell infiltrations. In this work, we normalize the…
Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions…
Astrophysical relativistic flow problems require high resolution three-dimensional numerical simulations. In this paper, we describe a new parallel three-dimensional code for simulations of special relativistic hydrodynamics (SRHD) using…
This paper studies finite volume schemes for scalar hyperbolic conservation laws on evolving hypersurfaces of $\mathbb{R}^3$. We compare theoretical schemes assuming knowledge of all geometric quantities to (practical) schemes defined on…
Accurate prediction of shallow water flows relies on precise bottom topography data, yet direct bathymetric surveys are expensive and time-consuming. In contrast, remote sensing platforms such as radar or satellite altimetry provide…
Particle tracking in biological imaging is concerned with reconstructing the trajectories, locations, or velocities of the targeting particles. The standard approach of particle tracking consists of two steps: first reconstructing…
Compact Runge-Kutta (cRK) methods are a class of high order methods for solving hyperbolic conservation laws characterized by their compact stencil including only immediate neighboring finite elements. A Compact Runge-Kutta flux…
Given a set of solution snapshots of a hyperbolic PDE, we are interested in learning a reduced order model (ROM). To this end, we propose a novel decompose then learn approach. We decompose the solution by expressing it as a composition of…
A framework for reconstruction of optical diffusion and absorption coefficients in quantitative photoacoustic tomography is presented. This framework is based on a Tikhonov-type functional with a regularization term promoting sparsity of…
We describe a single step, second-order accurate Godunov scheme for ideal MHD based on combining the piecewise parabolic method (PPM) for performing spatial reconstruction, the corner transport upwind (CTU) method of Colella for…
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet…