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Journal of Applied Meteorology (1962-1982), ISSN 0021-8952, 2/1970, Volume 9, Issue 1, pp. 149 - 153
.... The grid refinement technique, an iterative optimal path algorithm, is extended so that it can be applied to this class of optimal problem, and the results obtained for actual velocity fields... 
Speed | Travel time | Approximation | Navigation | Ships | Weather forecasting | Velocity distribution | Grid refinement | Waves | Meteorology
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 6/1970, Volume 7, Issue 2, pp. 199 - 205
...SlAM J. NUMER. ANAL. Vol. 7, No. 2, June 1970 MESH REFINEMENTS FOR THE HEAT EQUATION* STANLEY OSHER]" 1. Introduction. In a previous paper [4] we obtained... 
Integers | Boundary value problems | Approximation | Heat equation | Difference equations | Boundary conditions | Fourier transformations | Mathematical constants | Mathematics | Grid refinement
Journal Article
Mathematics of Computation, ISSN 0025-5718, 4/1971, Volume 25, Issue 114, pp. 219 - 227
We consider a finite-difference approximation to the Cauchy problem for a first-order hyperbolic partial differential equation using different mesh spacings in... 
Approximate values | Approximation | Algebra | Difference equations | Partial differential equations | Boundary conditions | Grid refinement | Cauchy problem | Nontrivial solutions
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 12/1972, Volume 9, Issue 4, pp. 695 - 701
.... A local regridding procedure for finite difference approxi mations, referred to as a mesh refinement scheme, was analyzed by the author in [1], I2] for hyperbolic... 
Sufficient conditions | Boundary value problems | Approximation | Difference equations | Partial differential equations | Eigenvalues | Boundary conditions | Grid refinement | Cauchy problem
Journal Article
Mathematics of Computation, ISSN 0025-5718, 1/1973, Volume 27, Issue 121, pp. 29 - 39
We study mesh refinement techniques for first-order hyperbolic equations. A refinement method for use with the leap-frog scheme is defined and its stability established... 
Mathematical intervals | Mathematical procedures | Wave propagation | Approximation | Wavelengths | Differential equations | Sine function | Boundary conditions | Grid refinement | Atmospherics
Journal Article
Mathematics of Computation, ISSN 0025-5718, 10/1973, Volume 27, Issue 124, pp. 745 - 754
Given certain implicit difference approximations to $u_t = a(x)u_{xx} + b(x)u_x + c(x)u$ in the region $- \infty < x < \infty, t \geqq 0$, with a finer... 
Boundary value problems | Approximation | Mathematical theorems | Difference equations | Variable coefficients | Boundary conditions | Coefficients | Grid refinement | Mesh refinement | Parabolic partial differential equation | Initial boundary-value problem | Difference scheme | Stability
Journal Article
NOAA TECHNICAL MEMORANDUM ERL WMPO-11, JANUARY 1974. 30 P, 12 FIG, 4 TAB, 9 REF. ALSO AS NHRL-107, 01/1974
NUMERICAL EXPERIMENTS WITH A MESH REFINEMENT TECHNIQUE ARE APPLIED TO THE FINITE DIFFERENCE EQUATIONS THAT REPRESENT ONE-DIMENSIONAL GRAVITY WAVE AND ADVECTION PHENOMENA... 
NUMERICAL ANALYSIS | PRESSURE | LINEAR ADVECTION | HURRICANES | GRID-MESH RATIO | MODEL STUDIES | GRAVITY WAVES | REFLECTED WAVES | ADVECTION | MONOCHROMATIC WAVES | NESTED GRIDS
Journal Article
SAE Transactions, ISSN 0096-736X, 1/1977, Volume 86, pp. 2211 - 2219
Much of the recent work by the author [1-5] as well as others [6-12] has focused on the need to consider idealization geometry a variable in the finite element... 
Idealization | Potential energy | Degrees of freedom | Mathematical concepts | Mathematical optima | Eigenvalues | Coordinate systems | Elastostatics | Isoenergetic processes | Grid refinement
Journal Article
Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, 6/1979, Volume 76, Issue 6, pp. 2499 - 2502
A ``projection function,'' P(x,z), is defined as the partial integral of the molecular electron density, ρ (x,y,z) over the region -∞ < y < +∞ The projection... 
Molecules | Oxygen | Atoms | Molecular orbitals | Mathematical functions | Electrical grids | Electron density | Carbon | Density | Electrons
Journal Article
Management Science, ISSN 0025-1909, 08/1979, Volume 25, Issue 8, pp. 744 - 753
Methodologies developed in the last several years allow formal inclusion of two sources of complexity in the analysis of a decision problem—uncertainty and... 
utility/preferences: multi-attribute | utility/preferences: estimation | Interpolation | Approximation | Computer software | Utility functions | Marginal utility | Assessed values | Mathematical constants | Grid refinement | preferences: estimation | preferences: multi-attribute; utility | utility
Journal Article
05/1980, Volume 23, Issue 5
The decision grid chart is investigated as an intermediate form in constructing decision tables; a very natural extension to the basic format is proposed. Five... 
systems design | decision grid chart | systems analysis | construction of compressed decision tables
Magazine Article
Proceedings of the 7th annual conference on computer graphics and interactive techniques, ISSN 0097-8930, 07/1980, pp. 117 - 123
This paper presents a new hidden surface algorithm. Its output is the set of the visible pieces of edges and faces, and is as accurate as the arithmetic... 
Algorithms analysis | Variable grid | Computational geometry | Computer graphics | Hidden line | Molecular models | Space-filling | Geometric intersections | Hidden surface
Conference Proceeding
Journal Article
Mathematical Programming, ISSN 0025-5610, 12/1980, Volume 19, Issue 1, pp. 78 - 91
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 05/1981, Volume 36, Issue 154, pp. 485 - 498
.... A discussion of the combined use of mesh refinement and a correction scheme multigrid technique is also provided... 
Boundary value problems | Approximation | Multigrid methods | Iterative solutions | Eigenvalues | Truncation errors | Eigenvectors | Grid refinement | Factorization
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 6/1982, Volume 19, Issue 3, pp. 548 - 560
The main objective of this paper is to treat the correction cycle of multigrid as a Newton-like method and to analyze it together with relaxation via a natural... 
Boundary value problems | Algebra | Approximation | Multigrid methods | Eigenvalues | Truncation errors | Mathematics | Design analysis | Stencils | Grid refinement | MATHEMATICS, APPLIED
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 6/1983, Volume 20, Issue 3, pp. 485 - 509
.... Moreover, the contribution of each element to this error allows to implement an automatic mesh refinement procedure leading to a uniform distribution of a given... 
Finite element method | Error rates | Mathematical procedures | Approximation | Equilibrium equations | Boundary conditions | Fees | Grid refinement | Vertices | Estimation methods
Journal Article
Journal of Computational Mathematics, ISSN 0254-9409, 10/1983, Volume 1, Issue 4, pp. 376 - 383
... for the extrapolation approximation based on mesh refinement and extrapolation is given. 
Mathematical extrapolation | Parallelograms | Triangulation | Estimate reliability | Approximation | Directional derivatives | Computational mathematics | Grid refinement | Point estimators | Estimation methods
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 6/1984, Volume 21, Issue 3, pp. 604 - 613
Mesh-refinement processes based on the generalized bisection of simplices are discussed and characterized in the context of the general theory of Rheinboldt [SIAM J. Numer. Anal., 17 (1980), pp. 766-778... 
Integers | Triangulation | Algorithms | Mathematical theorems | Triangles | Similarity theorem | Conformity | Grid refinement | Vertices
Journal Article
Journal of Metamorphic Geology, ISSN 0263-4929, 06/1985, Volume 3, Issue 2, pp. 137 - 153
.... Refinement of the average crystal structure in space group P4/nnc is consistent with occupancy of the A site with Al, of the half... 
Key‐words: petrogenetic grid | vesuvianite
Journal Article
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