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Results for “discontinuous spline”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

A Localized Tau Method PDE Solver

In this paper we present a new form of the collocation method that allows one to find very accurate solutions to time marching problems without the unwelcome appearance of Gibb's phenomenon oscillations. The basic method is applicable to any partial differential equation whose solution is a continuous, albeit possibly rapidly varying function. Discontinuous functions are dealt with by replacing the function in a small neighborhood of the discontinuity with a spline that smoothly connects the function segments on either side of the discontinuity. This will be demonstrated when the solution to the inviscid Burgers equation is discussed.

Cottam, Russell↗
NASA NTRS1989

Computing Viscoplastic Behavior Of A Material

Finite-element implementation developed for Robinson's unified model of viscoplasticity. Implemented via MARC general-purpose finite-element computer program by incorporating all of nonlinearity of material into initial load vector and treating vector as pseudo body force in finite-element equilibrium equations. In technique, each finite increment split into several equal subincrements, constitutive equations integrated by explicit Euler forward-difference method. HYPELA subroutine in MARC includes adaptive integration scheme selecting optimal sizes of subincrements. Spline function smooths discontinuous boundaries in Robinson's model to facilitate finite-element numerical calculations. Method used to calculate elastic, plastic, and creep deformations in solid materials at various temperatures; also used to study thermomechanical behavior of such things as hot pressure vessels and highly stressed components in engines.

Arya, V. K.↗
DOE OSTI2023

Fourier-informed knot placement schemes for B-spline approximation

Fitting B-splines to scientific data is especially challenging when the given data contain noise, jumps, or corners. Here, we describe how periodic data sets with these features can be efficiently approximated with B-splines by analyzing the Fourier spectrum of the data. Our method uses a collection of spectral filters to compute high-order derivatives, smoothed versions of noisy data, and the locations of jump discontinuities. Further, these quantities are then combined to choose knots that capture the qualitative features of the data, leading to accurate B-spline approximations with few knots. The method we introduce is direct and does not require any intermediate B-spline fitting before choosing the final knot distribution. Aside from fast Fourier transforms to transfer to and from Fourier space, the method runs in linear time with very little communication. We assess performance on several test cases in one and two dimensions, including data sets with jump discontinuities and noise. These tests show the method fits discontinuous data without spurious oscillations and remains effective in the presence of noise.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1984

Estimation of discontinuous coefficients in parabolic systems: Applications to reservoir simulation

Spline based techniques for estimating spatially varying parameters that appear in parabolic distributed systems (typical of those found in reservoir simulation problems) are presented. The problem of determining discontinuous coefficients, estimating both the functional shape and points of discontinuity for such parameters is discussed. Convergence results and a summary of numerical performance of the resulting algorithms are given.

Lamm, P. D.↗
NASA NTRS1987

Estimation of discontinuous coefficients in parabolic systems - Applications to reservoir simulation

Spline-based techniques for estimating spatially varying parameters that appear in parabolic distributed systems (typical of those found in reservoir simulation problems) are presented. In particular, the problem of determining discontinuous coefficients is discussed, estimating both the functional shape and points of discontinuity for such parameters. In addition, the ideas may also be applied to problems with unknown initial conditions and unknown parameters appearing in terms representing external forces. Convergence results and a summary of numerical performance of the resulting algorithms are given.

Lamm, Patricia K.↗
NASA NTRS1986

Partial spline models for the inclusion of tropopause and frontal boundary information in otherwise smooth two- and three-dimensional objective analysis

A new method, based on partial spline models, is developed for including specified discontinuities in otherwise smooth two- and three-dimensional objective analyses. The method is appropriate for including tropopause height information in two- and three-dimensinal temperature analyses, using the O'Sullivan-Wahba physical variational method for analysis of satellite radiance data, and may in principle be used in a combined variational analysis of observed, forecast, and climate information. A numerical method for its implementation is described and a prototype two-dimensional analysis based on simulated radiosonde and tropopause height data is shown. The method may also be appropriate for other geophysical problems, such as modeling the ocean thermocline, fronts, discontinuities, etc.

Shiau, Jyh-Jen↗
DOE OSTI2024

Accelerating Multivariate Functional Approximation Computation with Domain Decomposition Techniques⋆

Modeling large datasets through Multivariate Functional Approximations (MFA) provide an elegant way to handle many visualization and scientific analysis workflows. The process necessitates scalable data partitioning methods to compute MFA representations efficiently without compromising the accuracy or continuity of the reconstructed solution. We propose a domain -decomposed method for computing the MFA with B -spline bases, which reduces the total work per task and uses a restricted Additive Schwarz (RAS) method to converge the control point data degrees -of -freedom along subdomain boundaries. We provide an in-depth analysis of the parallel approach with domain decomposition solvers, aiming to minimize local subdomain error residuals and recover high -order continuity at subdomain interfaces with appropriate choices of knot overlaps. The communication cost, determined by the overlap regions in the RAS implementation, is optimized to recover the numerical error profile of the single subdomain case. Our proposed method stands in contrast to previous methods, which typically only recover either C 0 or at best C 1 continuity for arbitrary B -spline degree expansions, or those that require post -processing to blend discontinuities in the reconstructed data. We demonstrate the effectiveness of our approach using analytical and real -world datasets in 1D, 2D, and 3D through both strong and weak scaling studies. The performance results indicate that the overall cost of computing the approximation is directly proportional to the underlying nearest -neighbor communication implementation, and is only weakly dependent on the overlap region size that determines the size of the messages. This finding underscores the efficiency and scalability of our proposed method, making it a promising solution for handling large datasets in scientific workflows.

additive Schwarz solvers↗
NASA NTRS1986

Geomagnetic temporal change: 1903-1982 - A spline representation

The secular variation of the earth's magnetic field is itself subject to temporal variations. These are investigated with the aid of the coefficients of a series of spherical harmonic models of secular variation deduced from data for the interval 1903-1982 from the worldwide network of magnetic observatories. For some studies it is convenient to approximate the time variation of the spherical harmonic coefficients with a smooth, continuous, function; for this a spline fitting is used. The phenomena that are investigated include periodicities, discontinuities, and correlation with the length of day. The numerical data presented will be of use for further investigations and for the synthesis of secular variation at any place and at any time within the interval of the data - they are not appropriate for temporal extrapolations.

Langel, R. A.↗
NASA NTRS2003

Further Developments in the MLPG Method for Beam Problems

An accurate and yet simple Meshless Local Petrov-Galerkin (MLPG) formulation for analyzing beam problems is presented. In the formulation, simple weight functions are chosen as test functions as in the conventional MLPG method. Linear test functions are also chosen, leading to a variation of the MLPG method that is computationally efficient compared to the conventional implementation. The MLPG method is evaluated by applying the formulation to a variety of patch tests, thin beam problems, and problems with load discontinuities. The formulation successfully reproduces exact solutions to machine accuracy when higher order power and spline functions are chosen as test functions or when the linear test function is used, and when constructing the trial functions, the order of the basis function is properly balanced by the order of the weight function. For mixed boundary value problems, deflections, slopes, moments, and shear forces are calculated to the same accuracy by the MLPG method without the use of elaborate post-processing techniques. Problems with load discontinuities require special care - when a reasonable number of nodes are used, the method yields very accurate results.

Raju, I. S.↗
NASA NTRS1987

Quantitative analysis of the reconstruction performance of interpolants

The analysis presented provides a quantitative measure of the reconstruction or interpolation performance of linear, shift-invariant interpolants. The performance criterion is the mean square error of the difference between the sampled and reconstructed functions. The analysis is applicable to reconstruction algorithms used in image processing and to many types of splines used in numerical analysis and computer graphics. When formulated in the frequency domain, the mean square error clearly separates the contribution of the interpolation method from the contribution of the sampled data. The equations provide a rational basis for selecting an optimal interpolant; that is, one which minimizes the mean square error. The analysis has been applied to a selection of frequently used data splines and reconstruction algorithms: parametric cubic and quintic Hermite splines, exponential and nu splines (including the special case of the cubic spline), parametric cubic convolution, Keys' fourth-order cubic, and a cubic with a discontinuous first derivative. The emphasis in this paper is on the image-dependent case in which no a priori knowledge of the frequency spectrum of the sampled function is assumed.

Lansing, Donald L.↗
NASA NTRS1991

Algebraic grid generation for complex geometries

An efficient computer program called GRID2D/3D has been developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2D and 3D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation. The distribution of grid points within the spatial domain is controlled by stretching functions and grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For 2D spatial domains the boundary curves are constructed by using either cubic or tension spline interpolation. For 3D spatial domains the boundary surfaces are constructed by using a new technique, developed in this study, referred to as 3D bidirectional Hermite interpolation.

Shih, T. I.-P.↗
NASA NTRS2012

On Heatshield Shapes for Mars Entry Capsules

The 70deg sphere-cone - the standard geometry for all US Mars entry missions - is thoroughly examined via flow field simulations at a select few peak heating points along candidate flight trajectories. Emphasis is placed on turbulent heating based on the Baldwin- Lomax turbulence model. It is shown that increased leeward turbulent heating for a 70 sphere-cone flying at angle of attack is primarily due to the discontinuity in curvature between the spherical nose cap and the conical frustum - the attachment of the sonic line at this sphere-cone junction leads to a supersonic edge Mach number over the leeward acreage. In an attempt to mitigate this problem of elevated turbulent heating, alternate geometries, without any curvature discontinuities in the acreage, are developed. Two approaches, one based on nonlinear optimization with constraints, and one based on the use of non-uniform rational B-splines, are considered. All configurations examined remain axisymmetric. The aerothermal performance of alternate geometries is shown to be superior to that of the 70 sphere-cone.

Prabhu, DInesh K.↗
DOE OSTI2024

2-D seismic wave propagation using the distributional finite-difference method: further developments and potential for global seismology

SUMMARY We present a time-domain distributional finite-difference scheme based on the Lebedev staggered grid for the numerical simulation of wave propagation in acoustic and elastic media. The central aspect of the proposed method is the representation of the stresses and displacements with different sets of B-splines functions organized according to the staggered grid. The distributional finite-difference approach allows domain-decomposition, heterogeneity of the medium, curvilinear mesh, anisotropy, non-conformal interfaces, discontinuous grid and fluid–solid interfaces. Numerical examples show that the proposed scheme is suitable to model wave propagation through the Earth, where sharp interfaces separate large, relatively homogeneous layers. A few domains or elements are sufficient to represent the Earth’s internal structure without relying on advanced meshing techniques. We compare seismograms obtained with the proposed scheme and the spectral element method, and we show that our approach offers superior accuracy, reduced memory usage, and comparable efficiency.

Geochemistry & Geophysics↗
NASA NTRS1991

Integrated trajectory and control analysis for generic hypersonic vehicles

A tool which supports integrated assessment of air-breathing hypersonic vehicle trajectory management and control strategy has been developed by Hattis and Malchow (1991). Using a two-point boundary value problem solution technique, the tool can construct an entire near-minimum-fuel trajectory and desired control strategy from takeoff to orbit, while satisfying physically derived inequality constraints and while achieving efficient propulsive mode phasing. A strategy is also formulated to construct preliminary trajectory and control history representations with less computational burden than required for the overall flight profile assessment. A tabulated example hypersonic vehicle model has been used to demonstrate the integrated analysis methodology. To assure good numerical behavior when the algorithm uses tabulated model data, a multidimensional cubic spline curve smoothing routine has been developed. A dynamic-pressure-constrained, near-fuel-optimal trajectory was computed to provide examples of information that the methodology can provide. Previously unspecified propulsive discontinuities were located, flight regimes demanding rapid attitude changes were identified, available and closed-loop controller authority was ascertained, and inadequacies in vehicle and specific subsystem model representations were determined.

Hattis, Philip D.↗
NASA NTRS1995

A two dimensional interface element for coupling of independently modeled three dimensional finite element meshes and extensions to dynamic and non-linear regimes

The work reported here pertains only to the first year of research for a three year proposal period. As a prelude to this two dimensional interface element, the one dimensional element was tested and errors were discovered in the code for built-up structures and curved interfaces. These errors were corrected and the benchmark Boeing composite crown panel was analyzed successfully. A study of various splines led to the conclusion that cubic B-splines best suit this interface element application. A least squares approach combined with cubic B-splines was constructed to make a smooth function from the noisy data obtained with random error in the coordinate data points of the Boeing crown panel analysis. Preliminary investigations for the formulation of discontinuous 2-D shell and 3-D solid elements were conducted.

Aminpour, Mohammad↗
NASA NTRS1992

Coupled 2D-3D finite element method for analysis of a skin panel with a discontinuous stiffener

This paper describes a computationally efficient analysis method which was used to predict detailed stress states in a typical composite compression panel with a discontinuous hat stiffener. A global-local approach was used. The global model incorporated both 2D shell and 3D brick elements connected by newly developed transition elements. Most of the panel was modeled with 2D elements, while 3D elements were employed to model the stiffener flange and the adjacent skin. Both linear and geometrically nonlinear analyses were performed on the global model. The effect of geometric nonlinearity induced by the eccentric load path due to the discontinuous hat stiffener was significant. The local model used a fine mesh of 3D brick elements to model the region at the end of the stiffener. Boundary conditions of the local 3D model were obtained by spline interpolation of the nodal displacements from the global analysis. Detailed in-plane and through-the-thickness stresses were calculated in the flange-skin interface near the end of the stiffener.

Wang, J. T.↗
NASA NTRS2002

Meshless Local Petrov-Galerkin Method for Bending Problems

Recent literature shows extensive research work on meshless or element-free methods as alternatives to the versatile Finite Element Method. One such meshless method is the Meshless Local Petrov-Galerkin (MLPG) method. In this report, the method is developed for bending of beams - C1 problems. A generalized moving least squares (GMLS) interpolation is used to construct the trial functions, and spline and power weight functions are used as the test functions. The method is applied to problems for which exact solutions are available to evaluate its effectiveness. The accuracy of the method is demonstrated for problems with load discontinuities and continuous beam problems. A Petrov-Galerkin implementation of the method is shown to greatly reduce computational time and effort and is thus preferable over the previously developed Galerkin approach. The MLPG method for beam problems yields very accurate deflections and slopes and continuous moment and shear forces without the need for elaborate post-processing techniques.

Phillips, Dawn R.↗
NASA NTRS1988

Estimation of discontinuous coefficients and boundary parameters for hyperbolic systems

The problem of estimating discontinuous coefficients, including locations of discontinuities, that occur in second-order hyperbolic systems typical of those arising in one-dimensional surface seismic problems, is considered. The problem of identifying unknown parameters that appear in boundary conditions for the system is addressed. A spline-based approximation theory is presented as well as related convergence findings and representative numerical examples.

Lamm, Patricia K.↗