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Sunday, April 26, 2020 | History

3 edition of An adaptive grid algorithm for one-dimensional nonlinear equations found in the catalog.

An adaptive grid algorithm for one-dimensional nonlinear equations

An adaptive grid algorithm for one-dimensional nonlinear equations

  • 92 Want to read
  • 11 Currently reading

Published by National Aeronautics and Space Administration, National Technical Information Service, distributor in [Washington, DC, Springfield, Va .
Written in English

    Subjects:
  • Algorithms.

  • Edition Notes

    Other titlesAdaptive grid algorithm for one dimensional nonlinear equations.
    Statementsubmitted by William E. Gutierrez and Richard G. Hills.
    Series[NASA contractor report] -- NASA CR-190890.
    ContributionsHills, Richard G., United States. National Aeronautics and Space Administration.
    The Physical Object
    FormatMicroform
    Pagination1 v.
    ID Numbers
    Open LibraryOL14689565M

    An adaptive technique for estimating the minimal acceptable coarse grid size is proposed. Numerical experiments using full multigrid methods are performed on various one-dimensional second-order differential equations discretized on non-uniform grids, and the conditions under which they are convergent and efficient are studied. equations throughout the domain (hence do not turn the one­ dimensional trouble of boundary approx~ations into a two­ dimensiona~ trouble of complicated equa~ions). All these patches of local grids interact 'ttdth each other through the multi-grid process, which, at the same time, provides fast solu­. (source: Nielsen Book Data) A defining feature of nonlinear hyperbolic equations is the occurrence of shock waves. While the popular shock-capturing methods are easy to implement, shock-fitting techniques provide the most accurate results. A Shock-Fitting Primer presents the proper numerical treatment of shock waves and other discontinuities. YODA is an acronym for Yet anOther aDaptive Algorithm. The sequential version of the code was developed by Michel Mehrenberger and Martin Campos-Pinto during CEMRACS In we study a special type of solution for the one dimensional Vlasov-Maxwell equations. We assume Domain decomposition for the solution of nonlinear equations. This.


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An adaptive grid algorithm for one-dimensional nonlinear equations Download PDF EPUB FB2

A new fully numerical algorithm to solve one-dimensional convection-dominated PDE was proposed. • For the spatial discretization WENO schemes on non-uniform grids in a finite volume approach were used.

• Based on equidistribution principles and time-stepping control, the grid space and time step were dynamically adjusted. •Author: Fernando Ramírez-Correa, Miguel Á ngel Gómez-García, Izabela Dobrosz-Gómez, Carlos Alberto Rojas-Sie.

() New characteristic difference method with adaptive mesh for one-dimensional unsteady convection-dominated diffusion equations. International Journal of Computer Mathematics() Uniform pointwise convergence for a singularly Cited by: () Remapping-Free Adaptive GRP Method for Multi-Fluid Flows I: One Dimensional Euler Equations.

Communications in Computational Physics() A High-Order Accurate Gas-Kinetic Scheme for One- and Two-Dimensional Flow by: A method of adaptive grid refinement for the solution of the steady Euler equations for transonic flow is presented.

Algorithm automatically decides where the coarse grid accuracy is insufficient. An algorithm for creation of an optimized adaptive grid for improved explicit finite difference scheme Article (PDF Available) in WSEAS Transactions on Mathematics 7(9) January with 30 Reads.

A Wavelet-Based Adaptive Grid Method for the Resolution of Nonlinear PDEs Article in AIChE Journal 48(4) April with 18 Reads How we measure 'reads'. () An adaptive local mesh An adaptive grid algorithm for one-dimensional nonlinear equations book method for time-dependent partial differential equations.

Applied Numerical Mathematics() An adaptive moving grid method for one-dimensional systems of partial differential by: This paper investigates the solution of one-dimensional phase field models using an adaptive grid technique.

Three problems are considered: (1) the classical Stefan model, (2) the case of a solid sphere in equilibrium with its melt, and (3) a modified Stefan model with a generalized kinetic undercooling by: 4.

() An a posteriori based convergence analysis for a nonlinear singularly perturbed system of delay differential equations on an adaptive mesh. Numerical Algorithms() A robust adaptive grid method for a nonlinear singularly perturbed Cited by: In this work, we presented a new method by constructing a spectral approximation space adaptively based on a greedy algorithm for nonlinear differential equations.

(26) | α l →, i → | ≥ ϵ, for a so-called refinement threshold ϵ ≥ 0. Technically, the adaptive grid refinement can be built on top of the hierarchical grid structure. The points of the classical sparse grid form a tree-like data structure, as displayed in Fig.

4 for the one-dimensional case. Going from one level to the next, we see that there are two sons for each grid point (if l Cited by: 8. For this example, the monitor function is of the form with (α,β)=(6,).Using our moving mesh algorithm, we record data at t= (after singularity) with 30 2 and 60 2 grids.

In Fig. 7, the adaptive mesh and the approximation solutions are is seen that the problem is well resolved with 30 2 grid points, and the desired mesh adaptation effect is clearly by: This paper is the first part in a series of papers on adaptive finite element methods for parabolic problems.

In this paper, an adaptive algorithm is presented and analyzed for choosing the space and time discretization in a finite element method for a linear parabolic problem. The finite element method uses aspace discretization with meshsize variable in space and time and a third-order Cited by: A fully implicit, nonlinear adaptive grid strategy Article in Journal of Computational Physics March with 10 Reads How we measure 'reads'.

Get this from a library. An adaptive grid algorithm for one-dimensional nonlinear equations. [William E Gutierrez; Richard G Hills; United States. National Aeronautics and Space Administration.]. Adaptive moving grid methods for two-phase flow in porous media, J.

Comput. Appl. Math. An adaptive mesh redistribution method for nonlinear Hamilton-Jacobi equations in two- and three dimensions, J. Comput.

Phys. (), no. 2, A moving mesh algorithm for one-dimensional nonlinear hyperbolic conservation laws. An adaptive Huber method for nonlinear systems of Volterra integral equations with weakly singular kernels and solutions.

The present study is inspired by the class of one-dimensional Volterra integral equations (VIEs) (although the adaptive algorithm was found to operate satisfactorily also when the derivatives did not exist at t = 0).Cited by: 5. Adaptive moving grid strategies for one-dimensional systems of partial differential equations Conference Petzold, L R Recently a scheme has been proposed for choosing a moving mesh based on minimizing the time rate of change of the solution in the moving coordinates for one-dimensional systems of PDEs.

An adaptive multigrid method is presented for the solution of the two-dimensional steady state Van Roosbroeck equations for semiconductor device modeling. The discretisation is based on the (hybrid) mixed finite element method on by: 4.

Implicit Adaptive-Grid Radiation Hydrodynamics result in a grid distribution equidistant in either r or In r. Therefore the success of the ability of the grid to detect and resolve arbitrary structures in the flow depends heavily on the quality of the structure function fs, Cited by: Two-Grid based Adaptive Proper Orthogonal Decomposition Algorithm for Time Dependent Partial Differential Equations (with X.

Dai, X. Kuang, A. Zhou), arXiv preprint arXiv, Convergence analysis of stochastic structure-preserving schemes for computing effective diffusivity in random flows (with J. Lyu, Z.

Wang, Z. Zhang), arXiv. X. Ma, N. Zabaras, An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations. Comput. Phys. (8), – () MathSciNet CrossRef Google ScholarCited by: 3. This paper presents the development and verification of a computational algorithm to approximate the highly nonlinear transport equations of reactive chemical transport and multiphase flow.

The algorithm was developed based on the Lagrangian-Eulerian decoupling method with an adaptive ZOOMing and Peak/valley Capture (LEZOOMPC) scheme. Nakamura, S. Adaptive grid relocation algorithm for transonic full potential calculations using one-dimensional or two-dimensional diffusion equations.

In K. Ghia & U. Ghia (Eds.), Advances in grid generation (pp. 49–58). Houston: ASME. Google Scholar. R.M. Furzeland, J.G. Verwer & P.A. Zegeling, "A Numerical Study of Three Moving Grid Methods for One-Dimensional Partial Differential Equations Which Are Based on the Method of Lines"; published in "Journal of Computational Physics" (V89, pp.

). Verhulst & P.A. Zegeling, "An Asymptotic-Numerical Approach to the Coronal Loop Problem"; published in "Mathematical Methods. An Adaptive WENO Collocation Method for Differential Equations with Random Coefficients Since the singular curve is `dense’ in the one-dimensional space, the sparse grid algorithm will generate a `local’ tensor product grid around the curve in order to resolve such a singularity of the solution.

we developed an adaptive high-order Author: Wei Guo, Guang Lin, Andrew J. Christlieb, Jingmei Qiu. This is a survey on the theory of adaptive finite element methods (AFEM), which are fundamental in modern computational science and engineering.

We present a self-contained and up-to-date discussion of AFEM for linear second order elliptic partial differential equations (PDEs) and dimension d >1, with emphasis on the differences and advantages Cited by: A Generalized Feed-Forward Dynamic Adaptive Mesh Refinement and Derefinement Finite-Element Framework for Metal Laser Sintering—Part II: Nonlinear Thermal Simulations and Validations J.

Manuf. Sci. Eng (June, )Cited by: Uniform convergence of a Monotone iterative method for a nonlinear reaction-diffusion problem An adaptive-grid least squares finite element solution for flow in layered soils p.

Sensitivity analysis of generalized Lyapunov equations p. An algorithm to find values of minors of skew Hadamard and conference matrices p. dijkstra_openmp, a program which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.

disk_grid, a library which computes grid points within the interior of a disk of user specified radius and center in 2D, using GNUPLOT to create an image of the grid. A Fast Algorithm to Solve Non-Homogeneous Cauchy-Riemann Equations in the Complex Plane, Book of Abstracts, SIAM Annual Meeting, Washington D.C., Adaptive Computation of Porous Media Flow, Book of Abstracts, SIAM Annual Meeting, Chicago, Illinois, A New Method for One Dimensional Adaptive Grid Generation.

The Newton-CG method is a line search method: it finds a direction of search minimizing a quadratic approximation of the function and then uses a line search algorithm to find the (nearly) optimal step size in that direction.

An alternative approach is to, first, fix the step size limit \ (\Delta\) and then find the optimal step \ (\mathbf {p. The latter also contains an adaptive mesh procedure that has been enhanced here to resolve linear and nonlinear transport flow problems with steep fronts where regular FD and FE methods often fail.

An implicit first-order backward Euler and a third-order Taylor-Donea technique arc employed for Author: Manfred Koch. Two numerical schemes are developed for solutions of the bidimensional Maxwell-Bloch equations in nonlinear optical crystals.

The Maxwell-Bloch model was recently extended [C. Besse, B. Bidegaray, A. Bourgeade, P. Degond, O. Saut, A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals: an application to KDP, M2AN by: This paper presents a solution adaptive scheme for solving the Navier-Stokes equations on an unstructured mixed grid of triangles and quadrilaterals.

The solution procedure uses an explicit Runge-Kutta finite volume time marching scheme with an adaptive blend of second and fourth order by: 8.

YODA is an acronym for Yet anOther aDaptive Algorithm. The sequential version of the code was developed by Michel Mehrenberger and Martin Campos-Pinto during CEMRACS Domain decomposition for the solution of nonlinear equations. This a joint work with Noureddine Alaa, Professor at the Marrakech Cadi Ayyad University.

we present a. @article{osti_, title = {Adaptive Sparse Grid Construction in a Context of Local Anisotropy and Multiple Hierarchical Parents}, author = {Stoyanov, Miroslav K.}, abstractNote = {We consider general strategy for hierarchical multidimensional interpolation based on sparse grids, where the interpolation nodes and locally supported basis functions are constructed from tensors of a one.

In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued most basic version starts with a single-variable function f defined for a real variable x, the function's derivative f ′, and an.

No previous study has involved uncertain fractional differential equation (FDE, for short) with jump. In this paper, we propose the uncertain FDEs with jump, which is driven by both an uncertain V-jump process and an uncertain canonical of all, for the one-dimensional case, we give two types of uncertain FDEs with jump that are symmetric in terms of form.

The code solves the one-dimensional transient advection-diffusion equations pointed out the complexity of the algorithm’s book-keeping and the remaining difficulty in a priori choice of grid spacing. Ermakov oped an adaptive grid algorithm. The adaptive grid continuously.

The present article reviews recent progress for the application of B-spline collocation to fluid motion equations as well as new work in developing a novel adaptive knot insertion algorithm for a 1D convection-diffusion model equation.}, doi = {}, journal = {}, number =, volume =, place = {United States}, year = {Thu May 01 EDT @article{osti_, title = {A hyper-spherical adaptive sparse-grid method for high-dimensional discontinuity detection}, author = {Zhang, Guannan and Webster, Clayton G.

and Gunzburger, Max D. and Burkardt, John V.}, abstractNote = {This work proposes and analyzes a hyper-spherical adaptive hierarchical sparse-grid method for detecting jump.

Modified Euler–Lagrange Method for One Dimensional Advection (S W Armfield) An Analysis of the Spin-Up of a Convected Maxwell Fluid in a Rotational Rheometer Modified to Allow Axial Flow (D L Baker et al.) Heat Source Determination in Waste Rock Dumps (J M Barry) Numerical Solution of the Einstein Equations (R Bartnik & A Norton).