Introducing Differential Equations Students to the Fredholm Alternative--In Staggered Doses

ERIC Educational Resources Information Center

Savoye, Philippe

2011-01-01

The development, in an introductory differential equations course, of boundary value problems in parallel with initial value problems and the Fredholm Alternative. Examples are provided of pairs of homogeneous and nonhomogeneous boundary value problems for which existence and uniqueness issues are considered jointly. How this heightens students'…

Integrable boundary value problems for elliptic type Toda lattice in a disk

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guerses, Metin; Habibullin, Ismagil; Zheltukhin, Kostyantyn

The concept of integrable boundary value problems for soliton equations on R and R{sub +} is extended to regions enclosed by smooth curves. Classes of integrable boundary conditions in a disk for the Toda lattice and its reductions are found.

The Boundary Function Method. Fundamentals

NASA Astrophysics Data System (ADS)

Kot, V. A.

2017-03-01

The boundary function method is proposed for solving applied problems of mathematical physics in the region defined by a partial differential equation of the general form involving constant or variable coefficients with a Dirichlet, Neumann, or Robin boundary condition. In this method, the desired function is defined by a power polynomial, and a boundary function represented in the form of the desired function or its derivative at one of the boundary points is introduced. Different sequences of boundary equations have been set up with the use of differential operators. Systems of linear algebraic equations constructed on the basis of these sequences allow one to determine the coefficients of a power polynomial. Constitutive equations have been derived for initial boundary-value problems of all the main types. With these equations, an initial boundary-value problem is transformed into the Cauchy problem for the boundary function. The determination of the boundary function by its derivative with respect to the time coordinate completes the solution of the problem.

On the Formulation of Weakly Singular Displacement/Traction Integral Equations; and Their Solution by the MLPG Method

NASA Technical Reports Server (NTRS)

Atluri, Satya N.; Shen, Shengping

2002-01-01

In this paper, a very simple method is used to derive the weakly singular traction boundary integral equation based on the integral relationships for displacement gradients. The concept of the MLPG method is employed to solve the integral equations, especially those arising in solid mechanics. A moving Least Squares (MLS) interpolation is selected to approximate the trial functions in this paper. Five boundary integral Solution methods are introduced: direct solution method; displacement boundary-value problem; traction boundary-value problem; mixed boundary-value problem; and boundary variational principle. Based on the local weak form of the BIE, four different nodal-based local test functions are selected, leading to four different MLPG methods for each BIE solution method. These methods combine the advantages of the MLPG method and the boundary element method.

Stress-intensity factor calculations using the boundary force method

NASA Technical Reports Server (NTRS)

Tan, P. W.; Raju, I. S.; Newman, J. C., Jr.

1987-01-01

The Boundary Force Method (BFM) was formulated for the three fundamental problems of elasticity: the stress boundary value problem, the displacement boundary value problem, and the mixed boundary value problem. Because the BFM is a form of an indirect boundary element method, only the boundaries of the region of interest are modeled. The elasticity solution for the stress distribution due to concentrated forces and a moment applied at an arbitrary point in a cracked infinite plate is used as the fundamental solution. Thus, unlike other boundary element methods, here the crack face need not be modeled as part of the boundary. The formulation of the BFM is described and the accuracy of the method is established by analyzing a center-cracked specimen subjected to mixed boundary conditions and a three-hole cracked configuration subjected to traction boundary conditions. The results obtained are in good agreement with accepted numerical solutions. The method is then used to generate stress-intensity solutions for two common cracked configurations: an edge crack emanating from a semi-elliptical notch, and an edge crack emanating from a V-notch. The BFM is a versatile technique that can be used to obtain very accurate stress intensity factors for complex crack configurations subjected to stress, displacement, or mixed boundary conditions. The method requires a minimal amount of modeling effort.

Efficient algorithms for analyzing the singularly perturbed boundary value problems of fractional order

NASA Astrophysics Data System (ADS)

Sayevand, K.; Pichaghchi, K.

2018-04-01

In this paper, we were concerned with the description of the singularly perturbed boundary value problems in the scope of fractional calculus. We should mention that, one of the main methods used to solve these problems in classical calculus is the so-called matched asymptotic expansion method. However we shall note that, this was not achievable via the existing classical definitions of fractional derivative, because they do not obey the chain rule which one of the key elements of the matched asymptotic expansion method. In order to accommodate this method to fractional derivative, we employ a relatively new derivative so-called the local fractional derivative. Using the properties of local fractional derivative, we extend the matched asymptotic expansion method to the scope of fractional calculus and introduce a reliable new algorithm to develop approximate solutions of the singularly perturbed boundary value problems of fractional order. In the new method, the original problem is partitioned into inner and outer solution equations. The reduced equation is solved with suitable boundary conditions which provide the terminal boundary conditions for the boundary layer correction. The inner solution problem is next solved as a solvable boundary value problem. The width of the boundary layer is approximated using appropriate resemblance function. Some theoretical results are established and proved. Some illustrating examples are solved and the results are compared with those of matched asymptotic expansion method and homotopy analysis method to demonstrate the accuracy and efficiency of the method. It can be observed that, the proposed method approximates the exact solution very well not only in the boundary layer, but also away from the layer.

Initial-boundary value problems associated with the Ablowitz-Ladik system

NASA Astrophysics Data System (ADS)

Xia, Baoqiang; Fokas, A. S.

2018-02-01

We employ the Ablowitz-Ladik system as an illustrative example in order to demonstrate how to analyze initial-boundary value problems for integrable nonlinear differential-difference equations via the unified transform (Fokas method). In particular, we express the solutions of the integrable discrete nonlinear Schrödinger and integrable discrete modified Korteweg-de Vries equations in terms of the solutions of appropriate matrix Riemann-Hilbert problems. We also discuss in detail, for both the above discrete integrable equations, the associated global relations and the process of eliminating of the unknown boundary values.

NASA Ames three-dimensional potential flow analyses system (POTFAN) boundary condition code (BCDN), version 1

NASA Technical Reports Server (NTRS)

Davis, J. E.; Medan, R. T.

1977-01-01

This segment of the POTFAN system is used to generate right hand sides (boundary conditions) of the system of equations associated with the flow field under consideration. These specified flow boundary conditions are encountered in the oblique derivative boundary value problem (boundary value problem of the third kind) and contain the Neumann boundary condition as a special case. Arbitrary angle of attack and/or sideslip and/or rotation rates may be specified, as well as an arbitrary, nonuniform external flow field and the influence of prescribed singularity distributions.

Estimates of green tensors for certain boundary value problems

NASA Technical Reports Server (NTRS)

Solonnikov, V.

1988-01-01

Consider the first boundary value problem for a stationary Navier-Stokes system in a bounded three-dimensional region Omega with the boundary S: delta v = grad p+f, div v=0, v/s=0. Odqvist (1930) developed the potential theory and formulated the Green tensor for the above problem. The basic singular solution used by Odqvist to express the Green tensor is given. A theorem generalizing his results is presented along with four associated theorems. A specific problem associated with the study of the differential properties of the solution of stationary problems of magnetohydrodynamics is examined.

Extreme values and the level-crossing problem: An application to the Feller process

NASA Astrophysics Data System (ADS)

Masoliver, Jaume

2014-04-01

We review the question of the extreme values attained by a random process. We relate it to level crossings to one boundary (first-passage problems) as well as to two boundaries (escape problems). The extremes studied are the maximum, the minimum, the maximum absolute value, and the range or span. We specialize in diffusion processes and present detailed results for the Wiener and Feller processes.

Some boundary-value problems for anisotropic quarter plane

NASA Astrophysics Data System (ADS)

Arkhypenko, K. M.; Kryvyi, O. F.

2018-04-01

To solve the mixed boundary-value problems of the anisotropic elasticity for the anisotropic quarter plane, a method based on the use of the space of generalized functions {\\Im }{\\prime }({\\text{R}}+2) with slow growth properties was developed. The two-dimensional integral Fourier transform was used to construct the system of fundamental solutions for the anisotropic quarter plane in this space and a system of eight boundary integral relations was obtained, which allows one to reduce the mixed boundary-value problems for the anisotropic quarter plane directly to systems of singular integral equations with fixed singularities. The exact solutions of these systems were found by using the integral Mellin transform. The asymptotic behavior of solutions was investigated at the vertex of the quarter plane.

The complex variable boundary element method: Applications in determining approximative boundaries

USGS Publications Warehouse

Hromadka, T.V.

1984-01-01

The complex variable boundary element method (CVBEM) is used to determine approximation functions for boundary value problems of the Laplace equation such as occurs in potential theory. By determining an approximative boundary upon which the CVBEM approximator matches the desired constant (level curves) boundary conditions, the CVBEM is found to provide the exact solution throughout the interior of the transformed problem domain. Thus, the acceptability of the CVBEM approximation is determined by the closeness-of-fit of the approximative boundary to the study problem boundary. ?? 1984.

A Boundary Value Problem for Introductory Physics?

ERIC Educational Resources Information Center

Grundberg, Johan

2008-01-01

The Laplace equation has applications in several fields of physics, and problems involving this equation serve as paradigms for boundary value problems. In the case of the Laplace equation in a disc there is a well-known explicit formula for the solution: Poisson's integral. We show how one can derive this formula, and in addition two equivalent…

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: Stationary modes

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1988-01-01

Spatially discrete difference approximations for hyperbolic initial-boundary-value problems (IBVPs) require numerical boundary conditions in addition to the analytical boundary conditions specified for the differential equations. Improper treatment of a numerical boundary condition can cause instability of the discrete IBVP even though the approximation is stable for the pure initial-value or Cauchy problem. In the discrete IBVP stability literature there exists a small class of discrete approximations called borderline cases. For nondissipative approximations, borderline cases are unstable according to the theory of the Gustafsson, Kreiss, and Sundstrom (GKS) but they may be Lax-Richtmyer stable or unstable in the L sub 2 norm on a finite domain. It is shown that borderline approximation can be characterized by the presence of a stationary mode for the finite-domain problem. A stationary mode has the property that it does not decay with time and a nontrivial stationary mode leads to algebraic growth of the solution norm with mesh refinement. An analytical condition is given which makes it easy to detect a stationary mode; several examples of numerical boundary conditions are investigated corresponding to borderline cases.

Principal Eigenvalue Minimization for an Elliptic Problem with Indefinite Weight and Robin Boundary Conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hintermueller, M., E-mail: hint@math.hu-berlin.de; Kao, C.-Y., E-mail: Ckao@claremontmckenna.edu; Laurain, A., E-mail: laurain@math.hu-berlin.de

2012-02-15

This paper focuses on the study of a linear eigenvalue problem with indefinite weight and Robin type boundary conditions. We investigate the minimization of the positive principal eigenvalue under the constraint that the absolute value of the weight is bounded and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining the optimal spatial arrangement of favorable and unfavorable regions for a species to survive. For rectangular domains with Neumann boundary condition, it is known that there exists a threshold value such that if the total weight is below this thresholdmore » value then the optimal favorable region is like a section of a disk at one of the four corners; otherwise, the optimal favorable region is a strip attached to the shorter side of the rectangle. Here, we investigate the same problem with mixed Robin-Neumann type boundary conditions and study how this boundary condition affects the optimal spatial arrangement.« less

On some problems in a theory of thermally and mechanically interacting continuous media. Ph.D. Thesis; [linearized theory of interacting mixture of elastic solid and viscous fluid

NASA Technical Reports Server (NTRS)

Lee, Y. M.

1971-01-01

Using a linearized theory of thermally and mechanically interacting mixture of linear elastic solid and viscous fluid, we derive a fundamental relation in an integral form called a reciprocity relation. This reciprocity relation relates the solution of one initial-boundary value problem with a given set of initial and boundary data to the solution of a second initial-boundary value problem corresponding to a different initial and boundary data for a given interacting mixture. From this general integral relation, reciprocity relations are derived for a heat-conducting linear elastic solid, and for a heat-conducting viscous fluid. An initial-boundary value problem is posed and solved for the mixture of linear elastic solid and viscous fluid. With the aid of the Laplace transform and the contour integration, a real integral representation for the displacement of the solid constituent is obtained as one of the principal results of the analysis.

Completed Beltrami-Michell Formulation for Analyzing Radially Symmetrical Bodies

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Saigal, Sunil; Hopkins, Dale A.; Patnaik, Surya N.

1994-01-01

A force method formulation, the completed Beltrami-Michell formulation (CBMF), has been developed for analyzing boundary value problems in elastic continua. The CBMF is obtained by augmenting the classical Beltrami-Michell formulation with novel boundary compatibility conditions. It can analyze general elastic continua with stress, displacement, or mixed boundary conditions. The CBMF alleviates the limitations of the classical formulation, which can solve stress boundary value problems only. In this report, the CBMF is specialized for plates and shells. All equations of the CBMF, including the boundary compatibility conditions, are derived from the variational formulation of the integrated force method (IFM). These equations are defined only in terms of stresses. Their solution for kinematically stable elastic continua provides stress fields without any reference to displacements. In addition, a stress function formulation for plates and shells is developed by augmenting the classical Airy's formulation with boundary compatibility conditions expressed in terms of the stress function. The versatility of the CBMF and the augmented stress function formulation is demonstrated through analytical solutions of several mixed boundary value problems. The example problems include a composite circular plate and a composite circular cylindrical shell under the simultaneous actions of mechanical and thermal loads.

Numerical solution of the electron transport equation

NASA Astrophysics Data System (ADS)

Woods, Mark

The electron transport equation has been solved many times for a variety of reasons. The main difficulty in its numerical solution is that it is a very stiff boundary value problem. The most common numerical methods for solving boundary value problems are symmetric collocation methods and shooting methods. Both of these types of methods can only be applied to the electron transport equation if the boundary conditions are altered with unrealistic assumptions because they require too many points to be practical. Further, they result in oscillating and negative solutions, which are physically meaningless for the problem at hand. For these reasons, all numerical methods for this problem to date are a bit unusual because they were designed to try and avoid the problem of extreme stiffness. This dissertation shows that there is no need to introduce spurious boundary conditions or invent other numerical methods for the electron transport equation. Rather, there already exists methods for very stiff boundary value problems within the numerical analysis literature. We demonstrate one such method in which the fast and slow modes of the boundary value problem are essentially decoupled. This allows for an upwind finite difference method to be applied to each mode as is appropriate. This greatly reduces the number of points needed in the mesh, and we demonstrate how this eliminates the need to define new boundary conditions. This method is verified by showing that under certain restrictive assumptions, the electron transport equation has an exact solution that can be written as an integral. We show that the solution from the upwind method agrees with the quadrature evaluation of the exact solution. This serves to verify that the upwind method is properly solving the electron transport equation. Further, it is demonstrated that the output of the upwind method can be used to compute auroral light emissions.

Techniques for determining physical zones of influence

DOEpatents

Hamann, Hendrik F; Lopez-Marrero, Vanessa

2013-11-26

Techniques for analyzing flow of a quantity in a given domain are provided. In one aspect, a method for modeling regions in a domain affected by a flow of a quantity is provided which includes the following steps. A physical representation of the domain is provided. A grid that contains a plurality of grid-points in the domain is created. Sources are identified in the domain. Given a vector field that defines a direction of flow of the quantity within the domain, a boundary value problem is defined for each of one or more of the sources identified in the domain. Each of the boundary value problems is solved numerically to obtain a solution for the boundary value problems at each of the grid-points. The boundary problem solutions are post-processed to model the regions affected by the flow of the quantity on the physical representation of the domain.

Recursive recovery of Markov transition probabilities from boundary value data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patch, Sarah Kathyrn

1994-04-01

In an effort to mathematically describe the anisotropic diffusion of infrared radiation in biological tissue Gruenbaum posed an anisotropic diffusion boundary value problem in 1989. In order to accommodate anisotropy, he discretized the temporal as well as the spatial domain. The probabilistic interpretation of the diffusion equation is retained; radiation is assumed to travel according to a random walk (of sorts). In this random walk the probabilities with which photons change direction depend upon their previous as well as present location. The forward problem gives boundary value data as a function of the Markov transition probabilities. The inverse problem requiresmore » finding the transition probabilities from boundary value data. Problems in the plane are studied carefully in this thesis. Consistency conditions amongst the data are derived. These conditions have two effects: they prohibit inversion of the forward map but permit smoothing of noisy data. Next, a recursive algorithm which yields a family of solutions to the inverse problem is detailed. This algorithm takes advantage of all independent data and generates a system of highly nonlinear algebraic equations. Pluecker-Grassmann relations are instrumental in simplifying the equations. The algorithm is used to solve the 4 x 4 problem. Finally, the smallest nontrivial problem in three dimensions, the 2 x 2 x 2 problem, is solved.« less

A boundary-value problem for a first-order hyperbolic system in a two-dimensional domain

NASA Astrophysics Data System (ADS)

Zhura, N. A.; Soldatov, A. P.

2017-06-01

We consider a strictly hyperbolic first-order system of three equations with constant coefficients in a bounded piecewise-smooth domain. The boundary of the domain is assumed to consist of six smooth non-characteristic arcs. A boundary-value problem in this domain is posed by alternately prescribing one or two linear combinations of the components of the solution on these arcs. We show that this problem has a unique solution under certain additional conditions on the coefficients of these combinations, the boundary of the domain and the behaviour of the solution near the characteristics passing through the corner points of the domain.

The Ablowitz–Ladik system on a finite set of integers

NASA Astrophysics Data System (ADS)

Xia, Baoqiang

2018-07-01

We show how to solve initial-boundary value problems for integrable nonlinear differential–difference equations on a finite set of integers. The method we employ is the discrete analogue of the unified transform (Fokas method). The implementation of this method to the Ablowitz–Ladik system yields the solution in terms of the unique solution of a matrix Riemann–Hilbert problem, which has a jump matrix with explicit -dependence involving certain functions referred to as spectral functions. Some of these functions are defined in terms of the initial value, while the remaining spectral functions are defined in terms of two sets of boundary values. These spectral functions are not independent but satisfy an algebraic relation called global relation. We analyze the global relation to characterize the unknown boundary values in terms of the given initial and boundary values. We also discuss the linearizable boundary conditions.

Asymptotic solution of the problem for a thin axisymmetric cavern

NASA Technical Reports Server (NTRS)

Serebriakov, V. V.

1973-01-01

The boundary value problem which describes the axisymmetric separation of the flow around a body by a stationary infinite stream is considered. It is understood that the cavitation number varies over the length of the cavern. Using the asymptotic expansions for the potential of a thin body, the orders of magnitude of terms in the equations of the problem are estimated. Neglecting small quantities, a simplified boundary value problem is obtained.

Analytical methods for solving boundary value heat conduction problems with heterogeneous boundary conditions on lines. I - Review

NASA Astrophysics Data System (ADS)

Kartashov, E. M.

1986-10-01

Analytical methods for solving boundary value problems for the heat conduction equation with heterogeneous boundary conditions on lines, on a plane, and in space are briefly reviewed. In particular, the method of dual integral equations and summator series is examined with reference to stationary processes. A table of principal solutions to dual integral equations and pair summator series is proposed which presents the known results in a systematic manner. Newly obtained results are presented in addition to the known ones.

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Goldberg, M.; Tadmor, E.

1985-01-01

New convenient stability criteria are provided in this paper for a large class of finite difference approximations to initial-boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter plane x or = 0, t or = 0. Using the new criteria, stability is easily established for numerous combinations of well known basic schemes and boundary conditins, thus generalizing many special cases studied in recent literature.

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Goldberg, M.; Tadmor, E.

1983-01-01

New convenient stability criteria are provided in this paper for a large class of finite difference approximations to initial-boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter plane x or = 0, t or = 0. Using the new criteria, stability is easily established for numerous combinations of well known basic schemes and boundary conditions, thus generalizing many special cases studied in recent literature.

A collocation-shooting method for solving fractional boundary value problems

NASA Astrophysics Data System (ADS)

Al-Mdallal, Qasem M.; Syam, Muhammed I.; Anwar, M. N.

2010-12-01

In this paper, we discuss the numerical solution of special class of fractional boundary value problems of order 2. The method of solution is based on a conjugating collocation and spline analysis combined with shooting method. A theoretical analysis about the existence and uniqueness of exact solution for the present class is proven. Two examples involving Bagley-Torvik equation subject to boundary conditions are also presented; numerical results illustrate the accuracy of the present scheme.

[Kinetic theory and boundary conditions for highly inelastic spheres]. Quarterly progress report, April 1, 1993--June 30, 1993

DOE Office of Scientific and Technical Information (OSTI.GOV)

Richman, M.

1993-12-31

In this quarter, a kinetic theory was employed to set up the boundary value problem for steady, fully developed, gravity-driven flows of identical, smooth, highly inelastic spheres down bumpy inclines. The solid fraction, mean velocity, and components of the full second moment of fluctuation velocity were treated as mean fields. In addition to the balance equations for mass and momentum, the balance of the full second moment of fluctuation velocity was treated as an equation that must be satisfied by the mean fields. However, in order to simplify the resulting boundary value problem, fluxes of second moments in its isotropicmore » piece only were retained. The constitutive relations for the stresses and collisional source of second moment depend explicitly on the second moment of fluctuation velocity, and the constitutive relation for the energy flux depends on gradients of granular temperature, solid fraction, and components of the second moment. The boundary conditions require that the flows are free of stress and energy flux at their tops, and that momentum and energy are balanced at the bumpy base. The details of the boundary value problem are provided. In the next quarter, a solution procedure will be developed, and it will be employed to obtain sample numerical solutions to the boundary value problem described here.« less

Program for the solution of multipoint boundary value problems of quasilinear differential equations

NASA Technical Reports Server (NTRS)

1973-01-01

Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.

The first boundary-value problem for a fractional diffusion-wave equation in a non-cylindrical domain

NASA Astrophysics Data System (ADS)

Pskhu, A. V.

2017-12-01

We solve the first boundary-value problem in a non-cylindrical domain for a diffusion-wave equation with the Dzhrbashyan- Nersesyan operator of fractional differentiation with respect to the time variable. We prove an existence and uniqueness theorem for this problem, and construct a representation of the solution. We show that a sufficient condition for unique solubility is the condition of Hölder smoothness for the lateral boundary of the domain. The corresponding results for equations with Riemann- Liouville and Caputo derivatives are particular cases of results obtained here.

Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives

NASA Astrophysics Data System (ADS)

Antunes, Pedro R. S.; Ferreira, Rui A. C.

2017-07-01

In this work we study boundary value problems associated to a nonlinear fractional ordinary differential equation involving left and right Caputo derivatives. We discuss the regularity of the solutions of such problems and, in particular, give precise necessary conditions so that the solutions are C1([0, 1]). Taking into account our analytical results, we address the numerical solution of those problems by the augmented -RBF method. Several examples illustrate the good performance of the numerical method.

Integral Method of Boundary Characteristics: Neumann Condition

NASA Astrophysics Data System (ADS)

Kot, V. A.

2018-05-01

A new algorithm, based on systems of identical equalities with integral and differential boundary characteristics, is proposed for solving boundary-value problems on the heat conduction in bodies canonical in shape at a Neumann boundary condition. Results of a numerical analysis of the accuracy of solving heat-conduction problems with variable boundary conditions with the use of this algorithm are presented. The solutions obtained with it can be considered as exact because their errors comprise hundredths and ten-thousandths of a persent for a wide range of change in the parameters of a problem.

Theoretical investigations of plasma processes in the ion bombardment thruster

NASA Technical Reports Server (NTRS)

Wilhelm, H. E.

1975-01-01

A physical model for a thruster discharge was developed, consisting of a spatially diverging plasma sustained electrically between a small ring cathode and a larger ring anode in a cylindrical chamber with an axial magnetic field. The associated boundary-value problem for the coupled partial differential equations with mixed boundary conditions, which describe the electric potential and the plasma velocity fields, was solved in closed form. By means of quantum-mechanical perturbation theory, a formula for the number S(E) of atoms sputtered on the average by an ion of energy E was derived from first principles. The boundary-value problem describing the diffusion of the sputtered atoms through the surrounding rarefied electron-ion plasma to the system surfaces of ion propulsion systems was formulated and treated analytically. It is shown that outer boundary-value problems of this type lead to a complex integral equation, which requires numerical resolution.

Use of Green's functions in the numerical solution of two-point boundary value problems

NASA Technical Reports Server (NTRS)

Gallaher, L. J.; Perlin, I. E.

1974-01-01

This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system.

On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

NASA Astrophysics Data System (ADS)

BOERTJENS, G. J.; VAN HORSSEN, W. T.

2000-08-01

In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.

Similarity solution of the Boussinesq equation

NASA Astrophysics Data System (ADS)

Lockington, D. A.; Parlange, J.-Y.; Parlange, M. B.; Selker, J.

Similarity transforms of the Boussinesq equation in a semi-infinite medium are available when the boundary conditions are a power of time. The Boussinesq equation is reduced from a partial differential equation to a boundary-value problem. Chen et al. [Trans Porous Media 1995;18:15-36] use a hodograph method to derive an integral equation formulation of the new differential equation which they solve by numerical iteration. In the present paper, the convergence of their scheme is improved such that numerical iteration can be avoided for all practical purposes. However, a simpler analytical approach is also presented which is based on Shampine's transformation of the boundary value problem to an initial value problem. This analytical approximation is remarkably simple and yet more accurate than the analytical hodograph approximations.

A classical Perron method for existence of smooth solutions to boundary value and obstacle problems for degenerate-elliptic operators via holomorphic maps

NASA Astrophysics Data System (ADS)

Feehan, Paul M. N.

2017-09-01

We prove existence of solutions to boundary value problems and obstacle problems for degenerate-elliptic, linear, second-order partial differential operators with partial Dirichlet boundary conditions using a new version of the Perron method. The elliptic operators considered have a degeneracy along a portion of the domain boundary which is similar to the degeneracy of a model linear operator identified by Daskalopoulos and Hamilton [9] in their study of the porous medium equation or the degeneracy of the Heston operator [21] in mathematical finance. Existence of a solution to the partial Dirichlet problem on a half-ball, where the operator becomes degenerate on the flat boundary and a Dirichlet condition is only imposed on the spherical boundary, provides the key additional ingredient required for our Perron method. Surprisingly, proving existence of a solution to this partial Dirichlet problem with ;mixed; boundary conditions on a half-ball is more challenging than one might expect. Due to the difficulty in developing a global Schauder estimate and due to compatibility conditions arising where the ;degenerate; and ;non-degenerate boundaries; touch, one cannot directly apply the continuity or approximate solution methods. However, in dimension two, there is a holomorphic map from the half-disk onto the infinite strip in the complex plane and one can extend this definition to higher dimensions to give a diffeomorphism from the half-ball onto the infinite ;slab;. The solution to the partial Dirichlet problem on the half-ball can thus be converted to a partial Dirichlet problem on the slab, albeit for an operator which now has exponentially growing coefficients. The required Schauder regularity theory and existence of a solution to the partial Dirichlet problem on the slab can nevertheless be obtained using previous work of the author and C. Pop [16]. Our Perron method relies on weak and strong maximum principles for degenerate-elliptic operators, concepts of continuous subsolutions and supersolutions for boundary value and obstacle problems for degenerate-elliptic operators, and maximum and comparison principle estimates previously developed by the author [13].

COMPLEX VARIABLE BOUNDARY ELEMENT METHOD: APPLICATIONS.

USGS Publications Warehouse

Hromadka, T.V.; Yen, C.C.; Guymon, G.L.

1985-01-01

The complex variable boundary element method (CVBEM) is used to approximate several potential problems where analytical solutions are known. A modeling result produced from the CVBEM is a measure of relative error in matching the known boundary condition values of the problem. A CVBEM error-reduction algorithm is used to reduce the relative error of the approximation by adding nodal points in boundary regions where error is large. From the test problems, overall error is reduced significantly by utilizing the adaptive integration algorithm.

Resonances and vibrations in an elevator cable system due to boundary sway

NASA Astrophysics Data System (ADS)

Gaiko, Nick V.; van Horssen, Wim T.

2018-06-01

In this paper, an analytical method is presented to study an initial-boundary value problem describing the transverse displacements of a vertically moving beam under boundary excitation. The length of the beam is linearly varying in time, i.e., the axial, vertical velocity of the beam is assumed to be constant. The bending stiffness of the beam is assumed to be small. This problem may be regarded as a model describing the lateral vibrations of an elevator cable excited at its boundaries by the wind-induced building sway. Slow variation of the cable length leads to a singular perturbation problem which is expressed in slowly changing, time-dependent coefficients in the governing differential equation. By providing an interior layer analysis, infinitely many resonance manifolds are detected. Further, the initial-boundary value problem is studied in detail using a three-timescales perturbation method. The constructed formal approximations of the solutions are in agreement with the numerical results.

Numerical computations on one-dimensional inverse scattering problems

NASA Technical Reports Server (NTRS)

Dunn, M. H.; Hariharan, S. I.

1983-01-01

An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.

BOUNDARY VALUE PROBLEM INVOLVING THE p-LAPLACIAN ON THE SIERPIŃSKI GASKET

NASA Astrophysics Data System (ADS)

Priyadarshi, Amit; Sahu, Abhilash

In this paper, we study the following boundary value problem involving the weak p-Laplacian. -Δpu=λa(x)|u|q-1u + b(x)|u|l-1uin 𝒮∖𝒮 0; u=0on 𝒮0, where 𝒮 is the Sierpiński gasket in ℝ2, 𝒮0 is its boundary, λ > 0, p > 1, 0 < q < p - 1 < l and a,b : 𝒮→ ℝ are bounded nonnegative functions. We will show the existence of at least two nontrivial weak solutions to the above problem for a certain range of λ using the analysis of fibering maps on suitable subsets.

Boundary value problem for the solution of magnetic cutoff rigidities and some special applications

NASA Technical Reports Server (NTRS)

Edmonds, Larry

1987-01-01

Since a planet's magnetic field can sometimes provide a spacecraft with some protection against cosmic ray and solar flare particles, it is important to be able to quantify this protection. This is done by calculating cutoff rigidities. An alternate to the conventional method (particle trajectory tracing) is introduced, which is to treat the problem as a boundary value problem. In this approach trajectory tracing is only needed to supply boundary conditions. In some special cases, trajectory tracing is not needed at all because the problem can be solved analytically. A differential equation governing cutoff rigidities is derived for static magnetic fields. The presense of solid objects, which can block a trajectory and other force fields are not included. A few qualititative comments, on existence and uniqueness of solutions, are made which may be useful when deciding how the boundary conditions should be set up. Also included are topics on axially symmetric fields.

Elasto visco-plastic flow with special attention to boundary conditions

NASA Technical Reports Server (NTRS)

Shimazaki, Y.; Thompson, E. G.

1981-01-01

A simple but nontrivial steady-state creeping elasto visco-plastic (Maxwell fluid) radial flow problem is analyzed, with special attention given to the effects of the boundary conditions. Solutions are obtained through integration of a governing equation on stress using the Runge-Kutta method for initial value problems and finite differences for boundary value problems. A more general approach through the finite element method, an approach that solves for the velocity field rather than the stress field and that is applicable to a wide range of problems, is presented and tested using the radial flow example. It is found that steady-state flows of elasto visco-plastic materials are strongly influenced by the state of stress of material as it enters the region of interest. The importance of this boundary or initial condition in analyses involving materials coming into control volumes from unusual stress environments is emphasized.

Initial-Boundary Value Problem for Two-Component Gerdjikov-Ivanov Equation with 3 × 3 Lax Pair on Half-Line

NASA Astrophysics Data System (ADS)

Zhu, Qiao-Zhen; Fan, En-Gui; Xu, Jian

2017-10-01

The Fokas unified method is used to analyze the initial-boundary value problem of two-component Gerdjikov-Ivanonv equation on the half-line. It is shown that the solution of the initial-boundary problem can be expressed in terms of the solution of a 3 × 3 Riemann-Hilbert problem. The Dirichlet to Neumann map is obtained through the global relation. Supported by grants from the National Science Foundation of China under Grant No. 11671095, National Science Foundation of China under Grant No. 11501365, Shanghai Sailing Program supported by Science and Technology Commission of Shanghai Municipality under Grant No 15YF1408100, and the Hujiang Foundation of China (B14005)

On similarity solutions of a boundary layer problem with an upstream moving wall

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Lakin, W. D.; Nachman, A.

1986-01-01

The problem of a boundary layer on a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream is examined. It was previously shown that the solution of this boundary value problem is crucially dependent on the parameter which is the ratio of the velocity of the plate to the velocity of the free stream. In particular, it was proved that a solution exists only if this parameter does not exceed a certain critical value, and numerical evidence was adduced to show that this solution is nonunique. Using Crocco formulation the present work proves this nonuniqueness. Also considered are the analyticity of solutions and the derivation of upper bounds on the critical value of wall velocity parameter.

Numerical analysis of the asymptotic two-point boundary value solution for N-body trajectories.

NASA Technical Reports Server (NTRS)

Lancaster, J. E.; Allemann, R. A.

1972-01-01

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical boundary value solution applicable to a broad class of trajectory problems. In addition, the earlier first-order solutions have been extended to second-order to determine if improved accuracy is possible. Comparisons between the asymptotic solution and numerical integration for several lunar and interplanetary trajectories show that the asymptotic solution is generally quite accurate. Also, since no iterations are required, a solution to the boundary value problem is obtained in a fraction of the time required for numerically integrated solutions.

A Novel Numerical Method for Fuzzy Boundary Value Problems

NASA Astrophysics Data System (ADS)

Can, E.; Bayrak, M. A.; Hicdurmaz

2016-05-01

In the present paper, a new numerical method is proposed for solving fuzzy differential equations which are utilized for the modeling problems in science and engineering. Fuzzy approach is selected due to its important applications on processing uncertainty or subjective information for mathematical models of physical problems. A second-order fuzzy linear boundary value problem is considered in particular due to its important applications in physics. Moreover, numerical experiments are presented to show the effectiveness of the proposed numerical method on specific physical problems such as heat conduction in an infinite plate and a fin.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luo, Yousong, E-mail: yousong.luo@rmit.edu.au

This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.

A New Homotopy Perturbation Scheme for Solving Singular Boundary Value Problems Arising in Various Physical Models

NASA Astrophysics Data System (ADS)

Roul, Pradip; Warbhe, Ujwal

2017-08-01

The classical homotopy perturbation method proposed by J. H. He, Comput. Methods Appl. Mech. Eng. 178, 257 (1999) is useful for obtaining the approximate solutions for a wide class of nonlinear problems in terms of series with easily calculable components. However, in some cases, it has been found that this method results in slowly convergent series. To overcome the shortcoming, we present a new reliable algorithm called the domain decomposition homotopy perturbation method (DDHPM) to solve a class of singular two-point boundary value problems with Neumann and Robin-type boundary conditions arising in various physical models. Five numerical examples are presented to demonstrate the accuracy and applicability of our method, including thermal explosion, oxygen-diffusion in a spherical cell and heat conduction through a solid with heat generation. A comparison is made between the proposed technique and other existing seminumerical or numerical techniques. Numerical results reveal that only two or three iterations lead to high accuracy of the solution and this newly improved technique introduces a powerful improvement for solving nonlinear singular boundary value problems (SBVPs).

Boundary layers at the interface of two different shear flows

NASA Astrophysics Data System (ADS)

Weidman, Patrick D.; Wang, C. Y.

2018-05-01

We present solutions for the boundary layer between two uniform shear flows flowing in the same direction. In the upper layer, the flow has shear strength a, fluid density ρ1, and kinematic viscosity ν1, while the lower layer has shear strength b, fluid density ρ2, and kinematic viscosity ν2. Similarity transformations reduce the boundary-layer equations to a pair of ordinary differential equations governed by three dimensionless parameters: the shear strength ratio γ = b/a, the density ratio ρ = ρ2/ρ1, and the viscosity ratio ν = ν2/ν1. Further analysis shows that an affine transformation reduces this multi-parameter problem to a single ordinary differential equation which may be efficiently integrated as an initial-value problem. Solutions of the original boundary-value problem are shown to agree with the initial-value integrations, but additional dual and quadruple solutions are found using this method. We argue on physical grounds and through bifurcation analysis that these additional solutions are not tenable. The present problem is applicable to the trailing edge flow over a thin airfoil with camber.

Buffering effect in continuous chains of unidirectionally coupled generators

NASA Astrophysics Data System (ADS)

Glyzin, S. D.; Kolesov, A. Yu.; Rozov, N. Kh.

2014-11-01

We propose a mathematical model of a continuous annular chain of unidirectionally coupled generators given by some nonlinear advection-type hyperbolic boundary value problem. Such problems are constructed by a limit transition from annular chains of unidirectionally coupled ordinary differential equations with an unbounded increase in the number of links. We find that a certain buffering phenomenon is realized in our boundary value problem. Namely, we show that any preassigned finite number of stable periodic motions of the traveling-wave type can coexist in the model.

Geopotential coefficient determination and the gravimetric boundary value problem: A new approach

NASA Technical Reports Server (NTRS)

Sjoeberg, Lars E.

1989-01-01

New integral formulas to determine geopotential coefficients from terrestrial gravity and satellite altimetry data are given. The formulas are based on the integration of data over the non-spherical surface of the Earth. The effect of the topography to low degrees and orders of coefficients is estimated numerically. Formulas for the solution of the gravimetric boundary value problem are derived.

Well-posedness of nonlocal parabolic differential problems with dependent operators.

PubMed

Ashyralyev, Allaberen; Hanalyev, Asker

2014-01-01

The nonlocal boundary value problem for the parabolic differential equation v'(t) + A(t)v(t) = f(t) (0 ≤ t ≤ T), v(0) = v(λ) + φ, 0 < λ ≤ T in an arbitrary Banach space E with the dependent linear positive operator A(t) is investigated. The well-posedness of this problem is established in Banach spaces C 0 (β,γ) (E α-β ) of all E α-β -valued continuous functions φ(t) on [0, T] satisfying a Hölder condition with a weight (t + τ)(γ). New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.

On steady motion of viscoelastic fluid of Oldroyd type

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baranovskii, E. S., E-mail: esbaranovskii@gmail.com

2014-06-01

We consider a mathematical model describing the steady motion of a viscoelastic medium of Oldroyd type under the Navier slip condition at the boundary. In the rheological relation, we use the objective regularized Jaumann derivative. We prove the solubility of the corresponding boundary-value problem in the weak setting. We obtain an estimate for the norm of a solution in terms of the data of the problem. We show that the solution set is sequentially weakly closed. Furthermore, we give an analytic solution of the boundary-value problem describing the flow of a viscoelastic fluid in a flat channel under a slipmore » condition at the walls. Bibliography: 13 titles. (paper)« less

Application of shifted Jacobi pseudospectral method for solving (in)finite-horizon min-max optimal control problems with uncertainty

NASA Astrophysics Data System (ADS)

Nikooeinejad, Z.; Delavarkhalafi, A.; Heydari, M.

2018-03-01

The difficulty of solving the min-max optimal control problems (M-MOCPs) with uncertainty using generalised Euler-Lagrange equations is caused by the combination of split boundary conditions, nonlinear differential equations and the manner in which the final time is treated. In this investigation, the shifted Jacobi pseudospectral method (SJPM) as a numerical technique for solving two-point boundary value problems (TPBVPs) in M-MOCPs for several boundary states is proposed. At first, a novel framework of approximate solutions which satisfied the split boundary conditions automatically for various boundary states is presented. Then, by applying the generalised Euler-Lagrange equations and expanding the required approximate solutions as elements of shifted Jacobi polynomials, finding a solution of TPBVPs in nonlinear M-MOCPs with uncertainty is reduced to the solution of a system of algebraic equations. Moreover, the Jacobi polynomials are particularly useful for boundary value problems in unbounded domain, which allow us to solve infinite- as well as finite and free final time problems by domain truncation method. Some numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. A comparative study between the proposed method and other existing methods shows that the SJPM is simple and accurate.

Nonstationary Deformation of an Elastic Layer with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-11-01

The analytic solution to the plane problem for an elastic layer under a nonstationary surface load is found for mixed boundary conditions: normal stress and tangential displacement are specified on one side of the layer (fourth boundary-value problem of elasticity) and tangential stress and normal displacement are specified on the other side of the layer (second boundary-value problem of elasticity). The Laplace and Fourier integral transforms are applied. The inverse Laplace and Fourier transforms are found exactly using tabulated formulas and convolution theorems for various nonstationary loads. Explicit analytical expressions for stresses and displacements are derived. Loads applied to a constant surface area and to a surface area varying in a prescribed manner are considered. Computations demonstrate the dependence of the normal stress on time and spatial coordinates. Features of wave processes are analyzed

Nonsteady Problem for an Elastic Half-Plane with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-03-01

An approach to studying nonstationary wave processes in an elastic half-plane with mixed boundary conditions of the fourth boundary-value problem of elasticity is proposed. The Laplace and Fourier transforms are used. The sequential inversion of these transforms or the inversion of the joint transform by the Cagniard method allows obtaining the required solution (stresses, displacements) in a closed analytic form. With this approach, the problem can be solved for various types of loads

Computing Evans functions numerically via boundary-value problems

NASA Astrophysics Data System (ADS)

Barker, Blake; Nguyen, Rose; Sandstede, Björn; Ventura, Nathaniel; Wahl, Colin

2018-03-01

The Evans function has been used extensively to study spectral stability of travelling-wave solutions in spatially extended partial differential equations. To compute Evans functions numerically, several shooting methods have been developed. In this paper, an alternative scheme for the numerical computation of Evans functions is presented that relies on an appropriate boundary-value problem formulation. Convergence of the algorithm is proved, and several examples, including the computation of eigenvalues for a multi-dimensional problem, are given. The main advantage of the scheme proposed here compared with earlier methods is that the scheme is linear and scalable to large problems.

Two Legendre-Dual-Petrov-Galerkin Algorithms for Solving the Integrated Forms of High Odd-Order Boundary Value Problems

PubMed Central

Abd-Elhameed, Waleed M.; Doha, Eid H.; Bassuony, Mahmoud A.

2014-01-01

Two numerical algorithms based on dual-Petrov-Galerkin method are developed for solving the integrated forms of high odd-order boundary value problems (BVPs) governed by homogeneous and nonhomogeneous boundary conditions. Two different choices of trial functions and test functions which satisfy the underlying boundary conditions of the differential equations and the dual boundary conditions are used for this purpose. These choices lead to linear systems with specially structured matrices that can be efficiently inverted, hence greatly reducing the cost. The various matrix systems resulting from these discretizations are carefully investigated, especially their complexities and their condition numbers. Numerical results are given to illustrate the efficiency of the proposed algorithms, and some comparisons with some other methods are made. PMID:24616620

Towards Understanding the Mechanism of Receptivity and Bypass Dynamics in Laminar Boundary Layers

NASA Technical Reports Server (NTRS)

Lasseigne, D. G.; Criminale, W. O.; Joslin, R. D.; Jackson, T. L.

1999-01-01

Three problems concerning laminar-turbulent transition are addressed by solving a series of initial value problems. The first problem is the calculation of resonance within the continuous spectrum of the Blasius boundary layer. The second is calculation of the growth of Tollmien-Schlichting waves that are a direct result of disturbances that only lie outside of the boundary layer. And, the third problem is the calculation of non-parallel effects. Together, these problems represent a unified approach to the study of freestream disturbance effects that could lead to transition. Solutions to the temporal, initial-value problem with an inhomogeneous forcing term imposed upon the flow is sought. By solving a series of problems, it is shown that: A transient disturbance lying completely outside of the boundary layer can lead to the growth of an unstable Tollmien-Schlichting wave. A resonance with the continuous spectrum leads to strong amplification that may provide a mechanism for bypass transition once nonlinear effects are considered. A disturbance with a very weak unstable Tollmien-Schlichting wave can lead to a much stronger Tollmien-Schlichting wave downstream, if the original disturbance has a significant portion of its energy in the continuum modes.

SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-08-01

This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. Themore » notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.« less

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: An eigenvalue analysis

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1986-01-01

A hyperbolic initial-boundary-value problem can be approximated by a system of ordinary differential equations (ODEs) by replacing the spatial derivatives by finite-difference approximations. The resulting system of ODEs is called a semidiscrete approximation. A complication is the fact that more boundary conditions are required for the spatially discrete approximation than are specified for the partial differential equation. Consequently, additional numerical boundary conditions are required and improper treatment of these additional conditions can lead to instability. For a linear initial-boundary-value problem (IBVP) with homogeneous analytical boundary conditions, the semidiscrete approximation results in a system of ODEs of the form du/dt = Au whose solution can be written as u(t) = exp(At)u(O). Lax-Richtmyer stability requires that the matrix norm of exp(At) be uniformly bounded for O less than or = t less than or = T independent of the spatial mesh size. Although the classical Lax-Richtmyer stability definition involves a conventional vector norm, there is no known algebraic test for the uniform boundedness of the matrix norm of exp(At) for hyperbolic IBVPs. An alternative but more complicated stability definition is used in the theory developed by Gustafsson, Kreiss, and Sundstrom (GKS). The two methods are compared.

Mixed boundary-value problem for an orthotropic rectangular strip with variable coefficients of elasticity

NASA Astrophysics Data System (ADS)

Sargsyan, M. Z.; Poghosyan, H. M.

2018-04-01

A dynamical problem for a rectangular strip with variable coefficients of elasticity is solved by an asymptotic method. It is assumed that the strip is orthotropic, the elasticity coefficients are exponential functions of y, and mixed boundary conditions are posed. The solution of the inner problem is obtained using Bessel functions.

Optimal control and optimal trajectories of regional macroeconomic dynamics based on the Pontryagin maximum principle

NASA Astrophysics Data System (ADS)

Bulgakov, V. K.; Strigunov, V. V.

2009-05-01

The Pontryagin maximum principle is used to prove a theorem concerning optimal control in regional macroeconomics. A boundary value problem for optimal trajectories of the state and adjoint variables is formulated, and optimal curves are analyzed. An algorithm is proposed for solving the boundary value problem of optimal control. The performance of the algorithm is demonstrated by computing an optimal control and the corresponding optimal trajectories.

Boundary value problems with incremental plasticity in granular media

NASA Technical Reports Server (NTRS)

Chung, T. J.; Lee, J. K.; Costes, N. C.

1974-01-01

Discussion of the critical state concept in terms of an incremental theory of plasticity in granular (soil) media, and formulation of the governing equations which are convenient for a computational scheme using the finite element method. It is shown that the critical state concept with its representation by the classical incremental theory of plasticity can provide a powerful means for solving a wide variety of boundary value problems in soil media.

Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

NASA Technical Reports Server (NTRS)

Vaughan, William W.; Friedman, Mark J.; Monteiro, Anand C.

1993-01-01

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem.

Weak stability of the plasma-vacuum interface problem

NASA Astrophysics Data System (ADS)

Catania, Davide; D'Abbicco, Marcello; Secchi, Paolo

2016-09-01

We consider the free boundary problem for the two-dimensional plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region, the flow is governed by the usual compressible MHD equations, while in the vacuum region we consider the Maxwell system for the electric and the magnetic fields. At the free interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. We study the linear stability of rectilinear plasma-vacuum interfaces by computing the Kreiss-Lopatinskiĭ determinant of an associated linearized boundary value problem. Apart from possible resonances, we obtain that the piecewise constant plasma-vacuum interfaces are always weakly linearly stable, independently of the size of tangential velocity, magnetic and electric fields on both sides of the characteristic discontinuity. We also prove that solutions to the linearized problem obey an energy estimate with a loss of regularity with respect to the source terms, both in the interior domain and on the boundary, due to the failure of the uniform Kreiss-Lopatinskiĭ condition, as the Kreiss-Lopatinskiĭ determinant associated with this linearized boundary value problem has roots on the boundary of the frequency space. In the proof of the a priori estimates, a crucial part is played by the construction of symmetrizers for a reduced differential system, which has poles at which the Kreiss-Lopatinskiĭ condition may fail simultaneously.

New algorithms for solving third- and fifth-order two point boundary value problems based on nonsymmetric generalized Jacobi Petrov–Galerkin method

PubMed Central

Doha, E.H.; Abd-Elhameed, W.M.; Youssri, Y.H.

2014-01-01

Two families of certain nonsymmetric generalized Jacobi polynomials with negative integer indexes are employed for solving third- and fifth-order two point boundary value problems governed by homogeneous and nonhomogeneous boundary conditions using a dual Petrov–Galerkin method. The idea behind our method is to use trial functions satisfying the underlying boundary conditions of the differential equations and the test functions satisfying the dual boundary conditions. The resulting linear systems from the application of our method are specially structured and they can be efficiently inverted. The use of generalized Jacobi polynomials simplify the theoretical and numerical analysis of the method and also leads to accurate and efficient numerical algorithms. The presented numerical results indicate that the proposed numerical algorithms are reliable and very efficient. PMID:26425358

Numerical method for solving the nonlinear four-point boundary value problems

NASA Astrophysics Data System (ADS)

Lin, Yingzhen; Lin, Jinnan

2010-12-01

In this paper, a new reproducing kernel space is constructed skillfully in order to solve a class of nonlinear four-point boundary value problems. The exact solution of the linear problem can be expressed in the form of series and the approximate solution of the nonlinear problem is given by the iterative formula. Compared with known investigations, the advantages of our method are that the representation of exact solution is obtained in a new reproducing kernel Hilbert space and accuracy of numerical computation is higher. Meanwhile we present the convergent theorem, complexity analysis and error estimation. The performance of the new method is illustrated with several numerical examples.

Diffuse-interface polycrystal plasticity: expressing grain boundaries as geometrically necessary dislocations

NASA Astrophysics Data System (ADS)

Admal, Nikhil Chandra; Po, Giacomo; Marian, Jaime

2017-12-01

The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the system is modeled as a collection of boundary-value problems with matching boundary conditions. In this paper, we develop a diffuse-interface crystal plasticity model for polycrystalline materials that results in a single boundary-value problem with a single crystal as the reference configuration. Using a multiplicative decomposition of the deformation gradient into lattice and plastic parts, i.e. F( X,t)= F L( X,t) F P( X,t), an initial stress-free polycrystal is constructed by imposing F L to be a piecewise constant rotation field R 0( X), and F P= R 0( X)T, thereby having F( X,0)= I, and zero elastic strain. This model serves as a precursor to higher order crystal plasticity models with grain boundary energy and evolution.

Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects

NASA Astrophysics Data System (ADS)

Bian, Dongfen; Liu, Jitao

2017-12-01

This paper is concerned with the initial-boundary value problem to 2D magnetohydrodynamics-Boussinesq system with the temperature-dependent viscosity, thermal diffusivity and electrical conductivity. First, we establish the global weak solutions under the minimal initial assumption. Then by imposing higher regularity assumption on the initial data, we obtain the global strong solution with uniqueness. Moreover, the exponential decay rates of weak solutions and strong solution are obtained respectively.

Random deflections of a string on an elastic foundation.

NASA Technical Reports Server (NTRS)

Sanders, J. L., Jr.

1972-01-01

The paper is concerned with the problem of a taut string on a random elastic foundation subjected to random loads. The boundary value problem is transformed into an initial value problem by the method of invariant imbedding. Fokker-Planck equations for the random initial value problem are formulated and solved in some special cases. The analysis leads to a complete characterization of the random deflection function.

Solving transient acoustic boundary value problems with equivalent sources using a lumped parameter approach.

PubMed

Fahnline, John B

2016-12-01

An equivalent source method is developed for solving transient acoustic boundary value problems. The method assumes the boundary surface is discretized in terms of triangular or quadrilateral elements and that the solution is represented using the acoustic fields of discrete sources placed at the element centers. Also, the boundary condition is assumed to be specified for the normal component of the surface velocity as a function of time, and the source amplitudes are determined to match the known elemental volume velocity vector at a series of discrete time steps. Equations are given for marching-on-in-time schemes to solve for the source amplitudes at each time step for simple, dipole, and tripole source formulations. Several example problems are solved to illustrate the results and to validate the formulations, including problems with closed boundary surfaces where long-time numerical instabilities typically occur. A simple relationship between the simple and dipole source amplitudes in the tripole source formulation is derived so that the source radiates primarily in the direction of the outward surface normal. The tripole source formulation is shown to eliminate interior acoustic resonances and long-time numerical instabilities.

Time-Domain Impedance Boundary Conditions for Computational Aeroacoustics

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Auriault, Laurent

1996-01-01

It is an accepted practice in aeroacoustics to characterize the properties of an acoustically treated surface by a quantity known as impedance. Impedance is a complex quantity. As such, it is designed primarily for frequency-domain analysis. Time-domain boundary conditions that are the equivalent of the frequency-domain impedance boundary condition are proposed. Both single frequency and model broadband time-domain impedance boundary conditions are provided. It is shown that the proposed boundary conditions, together with the linearized Euler equations, form well-posed initial boundary value problems. Unlike ill-posed problems, they are free from spurious instabilities that would render time-marching computational solutions impossible.

Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method

NASA Astrophysics Data System (ADS)

Sohaib, Muhammad; Haq, Sirajul; Mukhtar, Safyan; Khan, Imad

2018-03-01

An efficient method is proposed to approximate sixth order boundary value problems. The proposed method is based on Legendre wavelet in which Legendre polynomial is used. The mechanism of the method is to use collocation points that converts the differential equation into a system of algebraic equations. For validation two test problems are discussed. The results obtained from proposed method are quite accurate, also close to exact solution, and other different methods. The proposed method is computationally more effective and leads to more accurate results as compared to other methods from literature.

The Use of Source-Sink and Doublet Distributions Extended to the Solution of Boundary-Value Problems in Supersonic Flow

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Lomax, Harvard

1948-01-01

A direct analogy is established between the use of source-sink and doublet distributions in the solution of specific boundary-value problems in subsonic wing theory and the corresponding problems in supersonic theory. The correct concept of the "finite part" of an integral is introduced and used in the calculation of the improper integrals associated with supersonic doublet distributions. The general equations developed are shown to include several previously published results and particular examples are given for the loading on rolling and pitching triangular wings with supersonic leading edges.

On Compressible Vortex Sheets

NASA Astrophysics Data System (ADS)

Secchi, Paolo

2005-05-01

We introduce the main known results of the theory of incompressible and compressible vortex sheets. Moreover, we present recent results obtained by the author with J. F. Coulombel about supersonic compressible vortex sheets in two space dimensions. The problem is a nonlinear free boundary hyperbolic problem with two difficulties: the free boundary is characteristic and the Lopatinski condition holds only in a weak sense, yielding losses of derivatives. Under a supersonic condition that precludes violent instabilities, we prove an energy estimate for the boundary value problem obtained by linearization around an unsteady piecewise solution.

New Boundary Constraints for Elliptic Systems used in Grid Generation Problems

NASA Technical Reports Server (NTRS)

Kaul, Upender K.; Clancy, Daniel (Technical Monitor)

2002-01-01

This paper discusses new boundary constraints for elliptic partial differential equations as used in grid generation problems in generalized curvilinear coordinate systems. These constraints, based on the principle of local conservation of thermal energy in the vicinity of the boundaries, are derived using the Green's Theorem. They uniquely determine the so called decay parameters in the source terms of these elliptic systems. These constraints' are designed for boundary clustered grids where large gradients in physical quantities need to be resolved adequately. It is observed that the present formulation also works satisfactorily for mild clustering. Therefore, a closure for the decay parameter specification for elliptic grid generation problems has been provided resulting in a fully automated elliptic grid generation technique. Thus, there is no need for a parametric study of these decay parameters since the new constraints fix them uniquely. It is also shown that for Neumann type boundary conditions, these boundary constraints uniquely determine the solution to the internal elliptic problem thus eliminating the non-uniqueness of the solution of an internal Neumann boundary value grid generation problem.

Flowing partially penetrating well: solution to a mixed-type boundary value problem

NASA Astrophysics Data System (ADS)

Cassiani, G.; Kabala, Z. J.; Medina, M. A.

A new semi-analytic solution to the mixed-type boundary value problem for a flowing partially penetrating well with infinitesimal skin situated in an anisotropic aquifer is developed. The solution is suited to aquifers having a semi-infinite vertical extent or to packer tests with aquifer horizontal boundaries far enough from the tested area. The problem reduces to a system of dual integral equations (DE) and further to a deconvolution problem. Unlike the analogous Dagan's steady-state solution [Water Resour. Res. 1978; 14:929-34], our DE solution does not suffer from numerical oscillations. The new solution is validated by matching the corresponding finite-difference solution and is computationally much more efficient. An automated (Newton-Raphson) parameter identification algorithm is proposed for field test inversion, utilizing the DE solution for the forward model. The procedure is computationally efficient and converges to correct parameter values. A solution for the partially penetrating flowing well with no skin and a drawdown-drawdown discontinuous boundary condition, analogous to that by Novakowski [Can. Geotech. J. 1993; 30:600-6], is compared to the DE solution. The D-D solution leads to physically inconsistent infinite total flow rate to the well, when no skin effect is considered. The DE solution, on the other hand, produces accurate results.

Review of Theoretical Approaches to Nonlinear Supercavitating Flows

DTIC Science & Technology

2001-02-01

hodograph) method to flow past a body with a curved topography was considered iy Levi - Civita [15] and Villat [24]. 2.3. Mixed boundary value problem...streamline flow around a body with a curved boundary 5.1. Levi - Civita approach Levi - Civita [15] was the first to propose an approach to solution of the plane...enotes a real parameter to 1)e determfineid. The second step is formulation of a imiixed bounidary value problem for Levi - Civita [15] function dw v WLC

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Goldberg, M.; Tadmor, E.

1986-01-01

The purpose of this paper is to achieve more versatile, convenient stability criteria for a wide class of finite-difference approximations to initial boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter-plane x greater than or equal to 0, t greater than or equal to 0. With these criteria, stability is easily established for a large number of examples, thus incorporating and generalizing many of the cases studied in recent literature.

The three-wave equation on the half-line

NASA Astrophysics Data System (ADS)

Xu, Jian; Fan, Engui

2014-01-01

The Fokas method is used to analyze the initial-boundary value problem for the three-wave equation p-{bi-bj}/{ai-aj}p+∑k ({bk-bj}/{ak-aj}-{bi-bk}/{ai-ak})pp=0, i,j,k=1,2,3, on the half-line. Assuming that the solution p(x,t) exists, we show that it can be recovered from its initial and boundary values via the solution of a Riemann-Hilbert problem formulated in the plane of the complex spectral parameter λ.

On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

NASA Astrophysics Data System (ADS)

Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich

2018-01-01

The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.

Bifurcation of solutions to Hamiltonian boundary value problems

NASA Astrophysics Data System (ADS)

McLachlan, R. I.; Offen, C.

2018-06-01

A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of equilibria, bifurcations of boundary value problems are global in nature and may not be related to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed framework which studies the bifurcations of critical points of functions. In this paper we study the bifurcations of solutions of boundary-value problems for symplectic maps, using the language of (finite-dimensional) singularity theory. We associate certain such problems with a geometric picture involving the intersection of Lagrangian submanifolds, and hence with the critical points of a suitable generating function. Within this framework, we then study the effect of three special cases: (i) some common boundary conditions, such as Dirichlet boundary conditions for second-order systems, restrict the possible types of bifurcations (for example, in generic planar systems only the A-series beginning with folds and cusps can occur); (ii) integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing symmetries can exhibit restricted bifurcations associated with the symmetry. This approach offers an alternative to the analysis of critical points in function spaces, typically used in the study of bifurcation of variational problems, and opens the way to the detection of more exotic bifurcations than the simple folds and cusps that are often found in examples.

A new Ellipsoidal Gravimetric-Satellite Altimetry Boundary Value Problem; Case study: High Resolution Geoid of Iran

NASA Astrophysics Data System (ADS)

Ardalan, A.; Safari, A.; Grafarend, E.

2003-04-01

A new ellipsoidal gravimetric-satellite altimetry boundary value problem has been developed and successfully tested. This boundary value problem has been constructed for gravity observables of the type (i) gravity potential (ii) gravity intensity (iii) deflection of vertical and (iv) satellite altimetry data. The developed boundary value problem is enjoying the ellipsoidal nature and as such can take advantage of high precision GPS observations in the set-up of the problem. The highlights of the solution are as follows: begin{itemize} Application of ellipsoidal harmonic expansion up to degree/order and ellipsoidal centrifugal field for the reduction of global gravity and isostasy effects from the gravity observable at the surface of the Earth. Application of ellipsoidal Newton integral on the equal area map projection surface for the reduction of residual mass effects within a radius of 55 km around the computational point. Ellipsoidal harmonic downward continuation of the residual observables from the surface of the earth down to the surface of reference ellipsoid using the ellipsoidal height of the observation points derived from GPS. Restore of the removed effects at the application points on the surface of reference ellipsoid. Conversion of the satellite altimetry derived heights of the water bodies into potential. Combination of the downward continued gravity information with the potential equivalent of the satellite altimetry derived heights of the water bodies. Application of ellipsoidal Bruns formula for converting the potential values on the surface of the reference ellipsoid into the geoidal heights (i.e. ellipsoidal heights of the geoid) with respect to the reference ellipsoid. Computation of the high-resolution geoid of Iran has successfully tested this new methodology!

BODYFIT-1FE: a computer code for three-dimensional steady-state/transient single-phase rod-bundle thermal-hydraulic analysis. Draft report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, B.C.J.; Sha, W.T.; Doria, M.L.

1980-11-01

The governing equations, i.e., conservation equations for mass, momentum, and energy, are solved as a boundary-value problem in space and an initial-value problem in time. BODYFIT-1FE code uses the technique of boundary-fitted coordinate systems where all the physical boundaries are transformed to be coincident with constant coordinate lines in the transformed space. By using this technique, one can prescribe boundary conditions accurately without interpolation. The transformed governing equations in terms of the boundary-fitted coordinates are then solved by using implicit cell-by-cell procedure with a choice of either central or upwind convective derivatives. It is a true benchmark rod-bundle code withoutmore » invoking any assumptions in the case of laminar flow. However, for turbulent flow, some empiricism must be employed due to the closure problem of turbulence modeling. The detailed velocity and temperature distributions calculated from the code can be used to benchmark and calibrate empirical coefficients employed in subchannel codes and porous-medium analyses.« less

ALGORITHM TO REDUCE APPROXIMATION ERROR FROM THE COMPLEX-VARIABLE BOUNDARY-ELEMENT METHOD APPLIED TO SOIL FREEZING.

USGS Publications Warehouse

Hromadka, T.V.; Guymon, G.L.

1985-01-01

An algorithm is presented for the numerical solution of the Laplace equation boundary-value problem, which is assumed to apply to soil freezing or thawing. The Laplace equation is numerically approximated by the complex-variable boundary-element method. The algorithm aids in reducing integrated relative error by providing a true measure of modeling error along the solution domain boundary. This measure of error can be used to select locations for adding, removing, or relocating nodal points on the boundary or to provide bounds for the integrated relative error of unknown nodal variable values along the boundary.

Existence of solutions of a two-dimensional boundary value problem for a system of nonlinear equations arising in growing cell populations.

PubMed

Jeribi, Aref; Krichen, Bilel; Mefteh, Bilel

2013-01-01

In the paper [A. Ben Amar, A. Jeribi, and B. Krichen, Fixed point theorems for block operator matrix and an application to a structured problem under boundary conditions of Rotenberg's model type, to appear in Math. Slovaca. (2014)], the existence of solutions of the two-dimensional boundary value problem (1) and (2) was discussed in the product Banach space L(p)×L(p) for p∈(1, ∞). Due to the lack of compactness on L1 spaces, the analysis did not cover the case p=1. The purpose of this work is to extend the results of Ben Amar et al. to the case p=1 by establishing new variants of fixed-point theorems for a 2×2 operator matrix, involving weakly compact operators.

Applying the method of fundamental solutions to harmonic problems with singular boundary conditions

NASA Astrophysics Data System (ADS)

Valtchev, Svilen S.; Alves, Carlos J. S.

2017-07-01

The method of fundamental solutions (MFS) is known to produce highly accurate numerical results for elliptic boundary value problems (BVP) with smooth boundary conditions, posed in analytic domains. However, due to the analyticity of the shape functions in its approximation basis, the MFS is usually disregarded when the boundary functions possess singularities. In this work we present a modification of the classical MFS which can be applied for the numerical solution of the Laplace BVP with Dirichlet boundary conditions exhibiting jump discontinuities. In particular, a set of harmonic functions with discontinuous boundary traces is added to the MFS basis. The accuracy of the proposed method is compared with the results form the classical MFS.

The application of MINIQUASI to thermal program boundary and initial value problems

NASA Technical Reports Server (NTRS)

1974-01-01

The feasibility of applying the solution techniques of Miniquasi to the set of equations which govern a thermoregulatory model is investigated. For solving nonlinear equations and/or boundary conditions, a Taylor Series expansion is required for linearization of both equations and boundary conditions. The solutions are iterative and in each iteration, a problem like the linear case is solved. It is shown that Miniquasi cannot be applied to the thermoregulatory model as originally planned.

Boundary layer flow of air over water on a flat plate

NASA Technical Reports Server (NTRS)

Nelson, John; Alving, Amy E.; Joseph, Daniel D.

1993-01-01

A non-similar boundary layer theory for air blowing over a water layer on a flat plate is formulated and studied as a two-fluid problem in which the position of the interface is unknown. The problem is considered at large Reynolds number (based on x), away from the leading edge. A simple non-similar analytic solution of the problem is derived for which the interface height is proportional to x(sub 1/4) and the water and air flow satisfy the Blasius boundary layer equations, with a linear profile in the water and a Blasius profile in the air. Numerical studies of the initial value problem suggests that this asymptotic, non-similar air-water boundary layer solution is a global attractor for all initial conditions.

Bifurcation approach to a logistic elliptic equation with a homogeneous incoming flux boundary condition

NASA Astrophysics Data System (ADS)

Umezu, Kenichiro

In this paper, we consider a semilinear elliptic boundary value problem in a smooth bounded domain, having the so-called logistic nonlinearity that originates from population dynamics, with a nonlinear boundary condition. Although the logistic nonlinearity has an absorption effect in the problem, the nonlinear boundary condition is induced by the homogeneous incoming flux on the boundary. The objective of our study is to analyze the existence of a bifurcation component of positive solutions from trivial solutions and its asymptotic behavior and stability. We perform this analysis using the method developed by Lyapunov and Schmidt, based on a scaling argument.

Second-Order Two-Sided Estimates in Nonlinear Elliptic Problems

NASA Astrophysics Data System (ADS)

Cianchi, Andrea; Maz'ya, Vladimir G.

2018-05-01

Best possible second-order regularity is established for solutions to p-Laplacian type equations with {p \\in (1, ∞)} and a square-integrable right-hand side. Our results provide a nonlinear counterpart of the classical L 2-coercivity theory for linear problems, which is missing in the existing literature. Both local and global estimates are obtained. The latter apply to solutions to either Dirichlet or Neumann boundary value problems. Minimal regularity on the boundary of the domain is required, although our conclusions are new even for smooth domains. If the domain is convex, no regularity of its boundary is needed at all.

High-order Two-way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering

NASA Technical Reports Server (NTRS)

Fibich, Gadi; Tsynkov, Semyon

2000-01-01

When solving linear scattering problems, one typically first solves for the impinging wave in the absence of obstacles. Then, by linear superposition, the original problem is reduced to one that involves only the scattered waves driven by the values of the impinging field at the surface of the obstacles. In addition, when the original domain is unbounded, special artificial boundary conditions (ABCs) that would guarantee the reflectionless propagation of waves have to be set at the outer boundary of the finite computational domain. The situation becomes conceptually different when the propagation equation is nonlinear. In this case the impinging and scattered waves can no longer be separated, and the problem has to be solved in its entirety. In particular, the boundary on which the incoming field values are prescribed, should transmit the given incoming waves in one direction and simultaneously be transparent to all the outgoing waves that travel in the opposite direction. We call this type of boundary conditions two-way ABCs. In the paper, we construct the two-way ABCs for the nonlinear Helmholtz equation that models the laser beam propagation in a medium with nonlinear index of refraction. In this case, the forward propagation is accompanied by backscattering, i.e., generation of waves in the direction opposite to that of the incoming signal. Our two-way ABCs generate no reflection of the backscattered waves and at the same time impose the correct values of the incoming wave. The ABCs are obtained for a fourth-order accurate discretization to the Helmholtz operator; the fourth-order grid convergence is corroborated experimentally by solving linear model problems. We also present solutions in the nonlinear case using the two-way ABC which, unlike the traditional Dirichlet boundary condition, allows for direct calculation of the magnitude of backscattering.

Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator

NASA Astrophysics Data System (ADS)

Vabishchevich, P. N.

2018-03-01

A time-dependent problem in a bounded domain for a fractional diffusion equation is considered. The first-order evolution equation involves a fractional-power second-order elliptic operator with Robin boundary conditions. A finite-element spatial approximation with an additive approximation of the operator of the problem is used. The time approximation is based on a vector scheme. The transition to a new time level is ensured by solving a sequence of standard elliptic boundary value problems. Numerical results obtained for a two-dimensional model problem are presented.

A Bifurcation Problem for a Nonlinear Partial Differential Equation of Parabolic Type,

DTIC Science & Technology

NONLINEAR DIFFERENTIAL EQUATIONS, INTEGRATION), (*PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS), BANACH SPACE , MAPPING (TRANSFORMATIONS), SET THEORY, TOPOLOGY, ITERATIONS, STABILITY, THEOREMS

A locally refined rectangular grid finite element method - Application to computational fluid dynamics and computational physics

NASA Technical Reports Server (NTRS)

Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Johnson, Forrester T.; Samant, Satish S.

1991-01-01

The present FEM technique addresses both linear and nonlinear boundary value problems encountered in computational physics by handling general three-dimensional regions, boundary conditions, and material properties. The box finite elements used are defined by a Cartesian grid independent of the boundary definition, and local refinements proceed by dividing a given box element into eight subelements. Discretization employs trilinear approximations on the box elements; special element stiffness matrices are included for boxes cut by any boundary surface. Illustrative results are presented for representative aerodynamics problems involving up to 400,000 elements.

On the solution of integral equations with a generalized Cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

A numerical technique is developed analytically to solve a class of singular integral equations occurring in mixed boundary-value problems for nonhomogeneous elastic media with discontinuities. The approach of Kaya and Erdogan (1987) is extended to treat equations with generalized Cauchy kernels, reformulating the boundary-value problems in terms of potentials as the unknown functions. The numerical implementation of the solution is discussed, and results for an epoxy-Al plate with a crack terminating at the interface and loading normal to the crack are presented in tables.

Conference on Ordinary and Partial Differential Equations, 29 March to 2 April 1982.

DTIC Science & Technology

1982-04-02

Azztr. Boundary value problems for elliptic and parabolic equations in domains with corners The paper concerns initial - Dirichlet and initial - mixed...boundary value problems for parabolic equations. a ij(x,t)u x + ai(x,t)Ux. + a(x,t)u-u = f(x,t) i3 1 x Xl,...,Xn , n 2. We consider the case of...moment II Though it is well known, that the electron possesses an anomalous magnetic moment, this term has not been considered so far in the mathematical

Metaheuristic optimisation methods for approximate solving of singular boundary value problems

NASA Astrophysics Data System (ADS)

Sadollah, Ali; Yadav, Neha; Gao, Kaizhou; Su, Rong

2017-07-01

This paper presents a novel approximation technique based on metaheuristics and weighted residual function (WRF) for tackling singular boundary value problems (BVPs) arising in engineering and science. With the aid of certain fundamental concepts of mathematics, Fourier series expansion, and metaheuristic optimisation algorithms, singular BVPs can be approximated as an optimisation problem with boundary conditions as constraints. The target is to minimise the WRF (i.e. error function) constructed in approximation of BVPs. The scheme involves generational distance metric for quality evaluation of the approximate solutions against exact solutions (i.e. error evaluator metric). Four test problems including two linear and two non-linear singular BVPs are considered in this paper to check the efficiency and accuracy of the proposed algorithm. The optimisation task is performed using three different optimisers including the particle swarm optimisation, the water cycle algorithm, and the harmony search algorithm. Optimisation results obtained show that the suggested technique can be successfully applied for approximate solving of singular BVPs.

Solutions of the benchmark problems by the dispersion-relation-preserving scheme

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Shen, H.; Kurbatskii, K. A.; Auriault, L.

1995-01-01

The 7-point stencil Dispersion-Relation-Preserving scheme of Tam and Webb is used to solve all the six categories of the CAA benchmark problems. The purpose is to show that the scheme is capable of solving linear, as well as nonlinear aeroacoustics problems accurately. Nonlinearities, inevitably, lead to the generation of spurious short wave length numerical waves. Often, these spurious waves would overwhelm the entire numerical solution. In this work, the spurious waves are removed by the addition of artificial selective damping terms to the discretized equations. Category 3 problems are for testing radiation and outflow boundary conditions. In solving these problems, the radiation and outflow boundary conditions of Tam and Webb are used. These conditions are derived from the asymptotic solutions of the linearized Euler equations. Category 4 problems involved solid walls. Here, the wall boundary conditions for high-order schemes of Tam and Dong are employed. These conditions require the use of one ghost value per boundary point per physical boundary condition. In the second problem of this category, the governing equations, when written in cylindrical coordinates, are singular along the axis of the radial coordinate. The proper boundary conditions at the axis are derived by applying the limiting process of r approaches 0 to the governing equations. The Category 5 problem deals with the numerical noise issue. In the present approach, the time-independent mean flow solution is computed first. Once the residual drops to the machine noise level, the incident sound wave is turned on gradually. The solution is marched in time until a time-periodic state is reached. No exact solution is known for the Category 6 problem. Because of this, the problem is formulated in two totally different ways, first as a scattering problem then as a direct simulation problem. There is good agreement between the two numerical solutions. This offers confidence in the computed results. Both formulations are solved as initial value problems. As such, no Kutta condition is required at the trailing edge of the airfoil.

Multiple Positive Solutions in the Second Order Autonomous Nonlinear Boundary Value Problems

NASA Astrophysics Data System (ADS)

Atslega, Svetlana; Sadyrbaev, Felix

2009-09-01

We construct the second order autonomous equations with arbitrarily large number of positive solutions satisfying homogeneous Dirichlet boundary conditions. Phase plane approach and bifurcation of solutions are the main tools.

SciCADE 95: International conference on scientific computation and differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

NONE

1995-12-31

This report consists of abstracts from the conference. Topics include algorithms, computer codes, and numerical solutions for differential equations. Linear and nonlinear as well as boundary-value and initial-value problems are covered. Various applications of these problems are also included.

Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations.

PubMed

Ercan, Ali; Kavvas, M Levent

2017-07-25

Scaling conditions to achieve self-similar solutions of 3-Dimensional (3D) Reynolds-Averaged Navier-Stokes Equations, as an initial and boundary value problem, are obtained by utilizing Lie Group of Point Scaling Transformations. By means of an open-source Navier-Stokes solver and the derived self-similarity conditions, we demonstrated self-similarity within the time variation of flow dynamics for a rigid-lid cavity problem under both up-scaled and down-scaled domains. The strength of the proposed approach lies in its ability to consider the underlying flow dynamics through not only from the governing equations under consideration but also from the initial and boundary conditions, hence allowing to obtain perfect self-similarity in different time and space scales. The proposed methodology can be a valuable tool in obtaining self-similar flow dynamics under preferred level of detail, which can be represented by initial and boundary value problems under specific assumptions.

A global time-dependent model of thunderstorm electricity. I - Mathematical properties of the physical and numerical models

NASA Technical Reports Server (NTRS)

Browning, G. L.; Tzur, I.; Roble, R. G.

1987-01-01

A time-dependent model is introduced that can be used to simulate the interaction of a thunderstorm with its global electrical environment. The model solves the continuity equation of the Maxwell current, which is assumed to be composed of the conduction, displacement, and source currents. Boundary conditions which can be used in conjunction with the continuity equation to form a well-posed initial-boundary value problem are determined. Properties of various components of solutions of the initial-boundary value problem are analytically determined. The results indicate that the problem has two time scales, one determined by the background electrical conductivity and the other by the time variation of the source function. A numerical method for obtaining quantitative results is introduced, and its properties are studied. Some simulation results on the evolution of the displacement and conduction currents during the electrification of a storm are presented.

Solvability of a fourth-order boundary value problem with periodic boundary conditions II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gupta, Chaitan P.

1991-01-01

Lemore » t f : [ 0 , 1 ] × R 4 → R be a function satisfying Caratheodory's conditions and e ( x ) ∈ L 1 [ 0 , 1 ] . This paper is concerned with the solvability of the fourth-order fully quasilinear boundary value problem d 4 u d x 4 + f ( x , u ( x ) , u ′ ( x ) , u ″ ( x ) , u ‴ ( x ) ) = e ( x ) ,    0 < x < 1 , with u ( 0 ) − u ( 1 ) = u ′ ( 0 ) − u ′ ( 1 ) = u ″ ( 0 ) - u ″ ( 1 ) = u ‴ ( 0 ) - u ‴ ( 1 ) = 0 . This problem was studied earlier by the author in the special case when f was of the form f ( x , u ( x ) ) , i.e., independent of u ′ ( x ) , u ″ ( x ) , u ‴ ( x ) . It turns out that the earlier methods do not apply in this general case. The conditions need to be related to both of the linear eigenvalue problems d 4 u d x 4 = λ 4 u and d 4 u d x 4 = − λ 2 d 2 u d x 2 with periodic boundary conditions.« less

A reciprocal theorem for a mixture theory. [development of linearized theory of interacting media

NASA Technical Reports Server (NTRS)

Martin, C. J.; Lee, Y. M.

1972-01-01

A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

On shifted Jacobi spectral method for high-order multi-point boundary value problems

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Hafez, R. M.

2012-10-01

This paper reports a spectral tau method for numerically solving multi-point boundary value problems (BVPs) of linear high-order ordinary differential equations. The construction of the shifted Jacobi tau approximation is based on conventional differentiation. This use of differentiation allows the imposition of the governing equation at the whole set of grid points and the straight forward implementation of multiple boundary conditions. Extension of the tau method for high-order multi-point BVPs with variable coefficients is treated using the shifted Jacobi Gauss-Lobatto quadrature. Shifted Jacobi collocation method is developed for solving nonlinear high-order multi-point BVPs. The performance of the proposed methods is investigated by considering several examples. Accurate results and high convergence rates are achieved.

A mesh gradient technique for numerical optimization

NASA Technical Reports Server (NTRS)

Willis, E. A., Jr.

1973-01-01

A class of successive-improvement optimization methods in which directions of descent are defined in the state space along each trial trajectory are considered. The given problem is first decomposed into two discrete levels by imposing mesh points. Level 1 consists of running optimal subarcs between each successive pair of mesh points. For normal systems, these optimal two-point boundary value problems can be solved by following a routine prescription if the mesh spacing is sufficiently close. A spacing criterion is given. Under appropriate conditions, the criterion value depends only on the coordinates of the mesh points, and its gradient with respect to those coordinates may be defined by interpreting the adjoint variables as partial derivatives of the criterion value function. In level 2, the gradient data is used to generate improvement steps or search directions in the state space which satisfy the boundary values and constraints of the given problem.

Quaternion regularization in celestial mechanics, astrodynamics, and trajectory motion control. III

NASA Astrophysics Data System (ADS)

Chelnokov, Yu. N.

2015-09-01

The present paper1 analyzes the basic problems arising in the solution of problems of the optimum control of spacecraft (SC) trajectory motion (including the Lyapunov instability of solutions of conjugate equations) using the principle of the maximum. The use of quaternion models of astrodynamics is shown to allow: (1) the elimination of singular points in the differential phase and conjugate equations and in their partial analytical solutions; (2) construction of the first integrals of the new quaternion; (3) a considerable decrease of the dimensions of systems of differential equations of boundary value optimization problems with their simultaneous simplification by using the new quaternion variables related with quaternion constants of motion by rotation transformations; (4) construction of general solutions of differential equations for phase and conjugate variables on the sections of SC passive motion in the simplest and most convenient form, which is important for the solution of optimum pulse SC transfers; (5) the extension of the possibilities of the analytical investigation of differential equations of boundary value problems with the purpose of identifying the basic laws of optimum control and motion of SC; (6) improvement of the computational stability of the solution of boundary value problems; (7) a decrease in the required volume of computation.

Estimation of the Thermal Process in the Honeycomb Panel by a Monte Carlo Method

NASA Astrophysics Data System (ADS)

Gusev, S. A.; Nikolaev, V. N.

2018-01-01

A new Monte Carlo method for estimating the thermal state of the heat insulation containing honeycomb panels is proposed in the paper. The heat transfer in the honeycomb panel is described by a boundary value problem for a parabolic equation with discontinuous diffusion coefficient and boundary conditions of the third kind. To obtain an approximate solution, it is proposed to use the smoothing of the diffusion coefficient. After that, the obtained problem is solved on the basis of the probability representation. The probability representation is the expectation of the functional of the diffusion process corresponding to the boundary value problem. The process of solving the problem is reduced to numerical statistical modelling of a large number of trajectories of the diffusion process corresponding to the parabolic problem. It was used earlier the Euler method for this object, but that requires a large computational effort. In this paper the method is modified by using combination of the Euler and the random walk on moving spheres methods. The new approach allows us to significantly reduce the computation costs.

Analytic solution for American strangle options using Laplace-Carson transforms

NASA Astrophysics Data System (ADS)

Kang, Myungjoo; Jeon, Junkee; Han, Heejae; Lee, Somin

2017-06-01

A strangle has been important strategy for options when the trader believes there will be a large movement in the underlying asset but are uncertain of which way the movement will be. In this paper, we derive analytic formula for the price of American strangle options. American strangle options can be mathematically formulated into the free boundary problems involving two early exercise boundaries. By using Laplace-Carson Transform(LCT), we can derive the nonlinear system of equations satisfied by the transformed value of two free boundaries. We then solve this nonlinear system using Newton's method and finally get the free boundaries and option values using numerical Laplace inversion techniques. We also derive the Greeks for the American strangle options as well as the value of perpetual American strangle options. Furthermore, we present various graphs for the free boundaries and option values according to the change of parameters.

Finite-volume application of high order ENO schemes to multi-dimensional boundary-value problems

NASA Technical Reports Server (NTRS)

Casper, Jay; Dorrepaal, J. Mark

1990-01-01

The finite volume approach in developing multi-dimensional, high-order accurate essentially non-oscillatory (ENO) schemes is considered. In particular, a two dimensional extension is proposed for the Euler equation of gas dynamics. This requires a spatial reconstruction operator that attains formal high order of accuracy in two dimensions by taking account of cross gradients. Given a set of cell averages in two spatial variables, polynomial interpolation of a two dimensional primitive function is employed in order to extract high-order pointwise values on cell interfaces. These points are appropriately chosen so that correspondingly high-order flux integrals are obtained through each interface by quadrature, at each point having calculated a flux contribution in an upwind fashion. The solution-in-the-small of Riemann's initial value problem (IVP) that is required for this pointwise flux computation is achieved using Roe's approximate Riemann solver. Issues to be considered in this two dimensional extension include the implementation of boundary conditions and application to general curvilinear coordinates. Results of numerical experiments are presented for qualitative and quantitative examination. These results contain the first successful application of ENO schemes to boundary value problems with solid walls.

Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

NASA Astrophysics Data System (ADS)

Chakrabarti, Aloknath; Mohapatra, Smrutiranjan

2013-09-01

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates, separated by a gap of finite width, floating horizontally on water of finite depth, are investigated in the present work for a two-dimensional time-harmonic case. Within the frame of linear water wave theory, the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions. Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem. In both the problems, the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates. Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations. The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration. The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

Solution of second order quasi-linear boundary value problems by a wavelet method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Lei; Zhou, Youhe; Wang, Jizeng, E-mail: jzwang@lzu.edu.cn

2015-03-10

A wavelet Galerkin method based on expansions of Coiflet-like scaling function bases is applied to solve second order quasi-linear boundary value problems which represent a class of typical nonlinear differential equations. Two types of typical engineering problems are selected as test examples: one is about nonlinear heat conduction and the other is on bending of elastic beams. Numerical results are obtained by the proposed wavelet method. Through comparing to relevant analytical solutions as well as solutions obtained by other methods, we find that the method shows better efficiency and accuracy than several others, and the rate of convergence can evenmore » reach orders of 5.8.« less

A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

PubMed

Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

2016-01-01

This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

Computational approach to Thornley's problem by bivariate operational calculus

NASA Astrophysics Data System (ADS)

Bazhlekova, E.; Dimovski, I.

2012-10-01

Thornley's problem is an initial-boundary value problem with a nonlocal boundary condition for linear onedimensional reaction-diffusion equation, used as a mathematical model of spiral phyllotaxis in botany. Applying a bivariate operational calculus we find explicit representation of the solution, containing two convolution products of special solutions and the arbitrary initial and boundary functions. We use a non-classical convolution with respect to the space variable, extending in this way the classical Duhamel principle. The special solutions involved are represented in the form of fast convergent series. Numerical examples are considered to show the application of the present technique and to analyze the character of the solution.

Numerical method for the solution of large systems of differential equations of the boundary layer type

NASA Technical Reports Server (NTRS)

Green, M. J.; Nachtsheim, P. R.

1972-01-01

A numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.

Asymptotic analysis of the narrow escape problem in dendritic spine shaped domain: three dimensions

NASA Astrophysics Data System (ADS)

Li, Xiaofei; Lee, Hyundae; Wang, Yuliang

2017-08-01

This paper deals with the three-dimensional narrow escape problem in a dendritic spine shaped domain, which is composed of a relatively big head and a thin neck. The narrow escape problem is to compute the mean first passage time of Brownian particles traveling from inside the head to the end of the neck. The original model is to solve a mixed Dirichlet-Neumann boundary value problem for the Poisson equation in the composite domain, and is computationally challenging. In this paper we seek to transfer the original problem to a mixed Robin-Neumann boundary value problem by dropping the thin neck part, and rigorously derive the asymptotic expansion of the mean first passage time with high order terms. This study is a nontrivial three-dimensional generalization of the work in Li (2014 J. Phys. A: Math. Theor. 47 505202), where a two-dimensional analogue domain is considered.

A method of boundary equations for unsteady hyperbolic problems in 3D

NASA Astrophysics Data System (ADS)

Petropavlovsky, S.; Tsynkov, S.; Turkel, E.

2018-07-01

We consider interior and exterior initial boundary value problems for the three-dimensional wave (d'Alembert) equation. First, we reduce a given problem to an equivalent operator equation with respect to unknown sources defined only at the boundary of the original domain. In doing so, the Huygens' principle enables us to obtain the operator equation in a form that involves only finite and non-increasing pre-history of the solution in time. Next, we discretize the resulting boundary equation and solve it efficiently by the method of difference potentials (MDP). The overall numerical algorithm handles boundaries of general shape using regular structured grids with no deterioration of accuracy. For long simulation times it offers sub-linear complexity with respect to the grid dimension, i.e., is asymptotically cheaper than the cost of a typical explicit scheme. In addition, our algorithm allows one to share the computational cost between multiple similar problems. On multi-processor (multi-core) platforms, it benefits from what can be considered an effective parallelization in time.

Eigenmode Analysis of Boundary Conditions for One-Dimensional Preconditioned Euler Equations

NASA Technical Reports Server (NTRS)

Darmofal, David L.

1998-01-01

An analysis of the effect of local preconditioning on boundary conditions for the subsonic, one-dimensional Euler equations is presented. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective with preconditioning, and, at low Mach numbers, disturbances do not decay. Other boundary conditions are investigated which are non-reflective with preconditioning and numerical results are presented confirming the analysis.

On the Boussinesq-Burgers equations driven by dynamic boundary conditions

NASA Astrophysics Data System (ADS)

Zhu, Neng; Liu, Zhengrong; Zhao, Kun

2018-02-01

We study the qualitative behavior of the Boussinesq-Burgers equations on a finite interval subject to the Dirichlet type dynamic boundary conditions. Assuming H1 ×H2 initial data which are compatible with boundary conditions and utilizing energy methods, we show that under appropriate conditions on the dynamic boundary data, there exist unique global-in-time solutions to the initial-boundary value problem, and the solutions converge to the boundary data as time goes to infinity, regardless of the magnitude of the initial data.

An Automatic Orthonormalization Method for Solving Stiff Boundary-Value Problems

NASA Astrophysics Data System (ADS)

Davey, A.

1983-08-01

A new initial-value method is described, based on a remark by Drury, for solving stiff linear differential two-point cigenvalue and boundary-value problems. The method is extremely reliable, it is especially suitable for high-order differential systems, and it is capable of accommodating realms of stiffness which other methods cannot reach. The key idea behind the method is to decompose the stiff differential operator into two non-stiff operators, one of which is nonlinear. The nonlinear one is specially chosen so that it advances an orthonormal frame, indeed the method is essentially a kind of automatic orthonormalization; the second is auxiliary but it is needed to determine the required function. The usefulness of the method is demonstrated by calculating some eigenfunctions for an Orr-Sommerfeld problem when the Reynolds number is as large as 10°.

Singularities of the quad curl problem

NASA Astrophysics Data System (ADS)

Nicaise, Serge

2018-04-01

We consider the quad curl problem in smooth and non smooth domains of the space. We first give an augmented variational formulation equivalent to the one from [25] if the datum is divergence free. We describe the singularities of the variational space which correspond to the ones of the Maxwell system with perfectly conducting boundary conditions. The edge and corner singularities of the solution of the corresponding boundary value problem with smooth data are also characterized. We finally obtain some regularity results of the variational solution.

Fixed Point Results for G-α-Contractive Maps with Application to Boundary Value Problems

PubMed Central

Roshan, Jamal Rezaei

2014-01-01

We unify the concepts of G-metric, metric-like, and b-metric to define new notion of generalized b-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes of G-α-admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, some examples and an application to the existence of a solution for the first-order periodic boundary value problem are provided here to illustrate the usability of the obtained results. PMID:24895655

On the initial-boundary value problem for some quasilinear parabolic equations of divergence form

NASA Astrophysics Data System (ADS)

Nakao, Mitsuhiro

2017-12-01

In this paper we give an existence theorem of global classical solution to the initial boundary value problem for the quasilinear parabolic equations of divergence form ut -div { σ (| ∇u|2) ∇u } = f (∇u , u , x , t) where σ (| ∇u|2) may not be bounded as | ∇u | → ∞. As an application the logarithmic type nonlinearity σ (| ∇u|2) = log ⁡ (1 + | ∇u|2) which is growing as | ∇u | → ∞ and degenerate at | ∇u | = 0 is considered under f ≡ 0.

A tensor Banach algebra approach to abstract kinetic equations

NASA Astrophysics Data System (ADS)

Greenberg, W.; van der Mee, C. V. M.

The study deals with a concrete algebraic construction providing the existence theory for abstract kinetic equation boundary-value problems, when the collision operator A is an accretive finite-rank perturbation of the identity operator in a Hilbert space H. An algebraic generalization of the Bochner-Phillips theorem is utilized to study solvability of the abstract boundary-value problem without any regulatory condition. A Banach algebra in which the convolution kernel acts is obtained explicitly, and this result is used to prove a perturbation theorem for bisemigroups, which then plays a vital role in solving the initial equations.

Solution of Poisson's Equation with Global, Local and Nonlocal Boundary Conditions

ERIC Educational Resources Information Center

Aliev, Nihan; Jahanshahi, Mohammad

2002-01-01

Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…

On solving wave equations on fixed bounded intervals involving Robin boundary conditions with time-dependent coefficients

NASA Astrophysics Data System (ADS)

van Horssen, Wim T.; Wang, Yandong; Cao, Guohua

2018-06-01

In this paper, it is shown how characteristic coordinates, or equivalently how the well-known formula of d'Alembert, can be used to solve initial-boundary value problems for wave equations on fixed, bounded intervals involving Robin type of boundary conditions with time-dependent coefficients. A Robin boundary condition is a condition that specifies a linear combination of the dependent variable and its first order space-derivative on a boundary of the interval. Analytical methods, such as the method of separation of variables (SOV) or the Laplace transform method, are not applicable to those types of problems. The obtained analytical results by applying the proposed method, are in complete agreement with those obtained by using the numerical, finite difference method. For problems with time-independent coefficients in the Robin boundary condition(s), the results of the proposed method also completely agree with those as for instance obtained by the method of separation of variables, or by the finite difference method.

COMOC: Three dimensional boundary region variant, programmer's manual

NASA Technical Reports Server (NTRS)

Orzechowski, J. A.; Baker, A. J.

1974-01-01

The three-dimensional boundary region variant of the COMOC computer program system solves the partial differential equation system governing certain three-dimensional flows of a viscous, heat conducting, multiple-species, compressible fluid including combustion. The solution is established in physical variables, using a finite element algorithm for the boundary value portion of the problem description in combination with an explicit marching technique for the initial value character. The computational lattice may be arbitrarily nonregular, and boundary condition constraints are readily applied. The theoretical foundation of the algorithm, a detailed description on the construction and operation of the program, and instructions on utilization of the many features of the code are presented.

On the Solution of Elliptic Partial Differential Equations on Regions with Corners

DTIC Science & Technology

2015-07-09

In this report we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations . We observe...that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of...efficient numerical algorithms. The results are illustrated by a number of numerical examples. On the solution of elliptic partial differential equations on

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

Singular boundary value problem for the integrodifferential equation in an insurance model with stochastic premiums: Analysis and numerical solution

NASA Astrophysics Data System (ADS)

Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

2012-10-01

A singular boundary value problem for a second-order linear integrodifferential equation with Volterra and non-Volterra integral operators is formulated and analyzed. The equation is defined on ℝ+, has a weak singularity at zero and a strong singularity at infinity, and depends on several positive parameters. Under natural constraints on the coefficients of the equation, existence and uniqueness theorems for this problem with given limit boundary conditions at singular points are proved, asymptotic representations of the solution are given, and an algorithm for its numerical determination is described. Numerical computations are performed and their interpretation is given. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer-Lundberg model with a stochastic process rate of premium under a certain investment strategy in the financial market. A comparative analysis of the results with those produced by the model with deterministic premiums is given.

Invariant characteristics of self-organization modes in Belousov reaction modeling

NASA Astrophysics Data System (ADS)

Glyzin, S. D.; Goryunov, V. E.; Kolesov, A. Yu

2018-01-01

We consider the problem of mathematical modeling of oxidation-reduction oscillatory chemical reactions based on the mechanism of Belousov reaction. The process of the main components interaction in such reaction can be interpreted by a phenomenologically similar to it “predator-prey” model. Thereby, we consider a parabolic boundary value problem consisting of three Volterra-type equations, which is a mathematical model of this reaction. We carry out a local study of the neighborhood of the system’s non-trivial equilibrium state and construct the normal form of the considering system. Finally, we do a numerical analysis of the coexisting chaotic oscillatory modes of the boundary value problem in a flat area, which have different nature and occur as the diffusion coefficient decreases.

Assessing the detail needed to capture rainfall-runoff dynamics with physics-based hydrologic response simulation

USGS Publications Warehouse

Mirus, B.B.; Ebel, B.A.; Heppner, C.S.; Loague, K.

2011-01-01

Concept development simulation with distributed, physics-based models provides a quantitative approach for investigating runoff generation processes across environmental conditions. Disparities within data sets employed to design and parameterize boundary value problems used in heuristic simulation inevitably introduce various levels of bias. The objective was to evaluate the impact of boundary value problem complexity on process representation for different runoff generation mechanisms. The comprehensive physics-based hydrologic response model InHM has been employed to generate base case simulations for four well-characterized catchments. The C3 and CB catchments are located within steep, forested environments dominated by subsurface stormflow; the TW and R5 catchments are located in gently sloping rangeland environments dominated by Dunne and Horton overland flows. Observational details are well captured within all four of the base case simulations, but the characterization of soil depth, permeability, rainfall intensity, and evapotranspiration differs for each. These differences are investigated through the conversion of each base case into a reduced case scenario, all sharing the same level of complexity. Evaluation of how individual boundary value problem characteristics impact simulated runoff generation processes is facilitated by quantitative analysis of integrated and distributed responses at high spatial and temporal resolution. Generally, the base case reduction causes moderate changes in discharge and runoff patterns, with the dominant process remaining unchanged. Moderate differences between the base and reduced cases highlight the importance of detailed field observations for parameterizing and evaluating physics-based models. Overall, similarities between the base and reduced cases indicate that the simpler boundary value problems may be useful for concept development simulation to investigate fundamental controls on the spectrum of runoff generation mechanisms. Copyright 2011 by the American Geophysical Union.

Dynamics and control of flexible spacecraft during and after slewing maneuvers

NASA Technical Reports Server (NTRS)

Kakad, Yogendra P.

1989-01-01

The dynamics and control of slewing maneuvers of NASA Spacecraft COntrol Laboratory Experiment (SCOLE) are analyzed. The control problem of slewing maneuvers of SCOLE is formulated in terms of an arbitrary maneuver about any given axis. The control system is developed for the combined problem of rigid-body slew maneuver and vibration suppression of the flexible appendage. The control problem formulation incorporates the nonlinear dynamical equations derived previously, and is expressed in terms of a two-point boundary value problem utilizing a quadratic type of performance index. The two-point boundary value problem is solved as a hierarchical control problem with the overall system being split in terms of two subsystems, namely the slewing of the entire assembly and the vibration suppression of the flexible antenna. The coupling variables between the two dynamical subsystems are identified and these two subsystems for control purposes are treated independently in parallel at the first level. Then the state-space trajectory of the combined problem is optimized at the second level.

Numerical reconstruction of unknown Robin inclusions inside a heat conductor by a non-iterative method

NASA Astrophysics Data System (ADS)

Nakamura, Gen; Wang, Haibing

2017-05-01

Consider the problem of reconstructing unknown Robin inclusions inside a heat conductor from boundary measurements. This problem arises from active thermography and is formulated as an inverse boundary value problem for the heat equation. In our previous works, we proposed a sampling-type method for reconstructing the boundary of the Robin inclusion and gave its rigorous mathematical justification. This method is non-iterative and based on the characterization of the solution to the so-called Neumann- to-Dirichlet map gap equation. In this paper, we give a further investigation of the reconstruction method from both the theoretical and numerical points of view. First, we clarify the solvability of the Neumann-to-Dirichlet map gap equation and establish a relation of its solution to the Green function associated with an initial-boundary value problem for the heat equation inside the Robin inclusion. This naturally provides a way of computing this Green function from the Neumann-to-Dirichlet map and explains what is the input for the linear sampling method. Assuming that the Neumann-to-Dirichlet map gap equation has a unique solution, we also show the convergence of our method for noisy measurements. Second, we give the numerical implementation of the reconstruction method for two-dimensional spatial domains. The measurements for our inverse problem are simulated by solving the forward problem via the boundary integral equation method. Numerical results are presented to illustrate the efficiency and stability of the proposed method. By using a finite sequence of transient input over a time interval, we propose a new sampling method over the time interval by single measurement which is most likely to be practical.

Group invariant solution for a pre-existing fracture driven by a power-law fluid in impermeable rock

NASA Astrophysics Data System (ADS)

Fareo, A. G.; Mason, D. P.

2013-12-01

The effect of power-law rheology on hydraulic fracturing is investigated. The evolution of a two-dimensional fracture with non-zero initial length and driven by a power-law fluid is analyzed. Only fluid injection into the fracture is considered. The surrounding rock mass is impermeable. With the aid of lubrication theory and the PKN approximation a partial differential equation for the fracture half-width is derived. Using a linear combination of the Lie-point symmetry generators of the partial differential equation, the group invariant solution is obtained and the problem is reduced to a boundary value problem for an ordinary differential equation. Exact analytical solutions are derived for hydraulic fractures with constant volume and with constant propagation speed. The asymptotic solution near the fracture tip is found. The numerical solution for general working conditions is obtained by transforming the boundary value problem to a pair of initial value problems. Throughout the paper, hydraulic fracturing with shear thinning, Newtonian and shear thickening fluids are compared.

Well-posedness of characteristic symmetric hyperbolic systems

NASA Astrophysics Data System (ADS)

Secchi, Paolo

1996-06-01

We consider the initial-boundary-value problem for quasi-linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity. We show the well-posedness in Hadamard's sense (i.e., existence, uniqueness and continuous dependence of solutions on the data) of regular solutions in suitable functions spaces which take into account the loss of regularity in the normal direction to the characteristic boundary.

Generic short-time propagation of sharp-boundaries wave packets

NASA Astrophysics Data System (ADS)

Granot, E.; Marchewka, A.

2005-11-01

A general solution to the "shutter" problem is presented. The propagation of an arbitrary initially bounded wave function is investigated, and the general solution for any such function is formulated. It is shown that the exact solution can be written as an expression that depends only on the values of the function (and its derivatives) at the boundaries. In particular, it is shown that at short times (t << 2mx2/hbar, where x is the distance to the boundaries) the wave function propagation depends only on the wave function's values (or its derivatives) at the boundaries of the region. Finally, we generalize these findings to a non-singular wave function (i.e., for wave packets with finite-width boundaries) and suggest an experimental verification.

Parallel computation using boundary elements in solid mechanics

NASA Technical Reports Server (NTRS)

Chien, L. S.; Sun, C. T.

1990-01-01

The inherent parallelism of the boundary element method is shown. The boundary element is formulated by assuming the linear variation of displacements and tractions within a line element. Moreover, MACSYMA symbolic program is employed to obtain the analytical results for influence coefficients. Three computational components are parallelized in this method to show the speedup and efficiency in computation. The global coefficient matrix is first formed concurrently. Then, the parallel Gaussian elimination solution scheme is applied to solve the resulting system of equations. Finally, and more importantly, the domain solutions of a given boundary value problem are calculated simultaneously. The linear speedups and high efficiencies are shown for solving a demonstrated problem on Sequent Symmetry S81 parallel computing system.

On flows of viscoelastic fluids under threshold-slip boundary conditions

NASA Astrophysics Data System (ADS)

Baranovskii, E. S.

2018-03-01

We investigate a boundary-value problem for the steady isothermal flow of an incompressible viscoelastic fluid of Oldroyd type in a 3D bounded domain with impermeable walls. We use the Fujita threshold-slip boundary condition. This condition states that the fluid can slip along a solid surface when the shear stresses reach a certain critical value; otherwise the slipping velocity is zero. Assuming that the flow domain is not rotationally symmetric, we prove an existence theorem for the corresponding slip problem in the framework of weak solutions. The proof uses methods for solving variational inequalities with pseudo-monotone operators and convex functionals, the method of introduction of auxiliary viscosity, as well as a passage-to-limit procedure based on energy estimates of approximate solutions, Korn’s inequality, and compactness arguments. Also, some properties and estimates of weak solutions are established.

A new method for determining acoustic-liner admittance in a rectangular duct with grazing flow from experimental data

NASA Technical Reports Server (NTRS)

Watson, W. R.

1984-01-01

A method is developed for determining acoustic liner admittance in a rectangular duct with grazing flow. The axial propagation constant, cross mode order, and mean flow profile is measured. These measured data are then input into an analytical program which determines the unknown admittance value. The analytical program is based upon a finite element discretization of the acoustic field and a reposing of the unknown admittance value as a linear eigenvalue problem on the admittance value. Gaussian elimination is employed to solve this eigenvalue problem. The method used is extendable to grazing flows with boundary layers in both transverse directions of an impedance tube (or duct). Predicted admittance values are compared both with exact values that can be obtained for uniform mean flow profiles and with those from a Runge Kutta integration technique for cases involving a one dimensional boundary layer.

On the existence of solutions to a one-dimensional degenerate nonlinear wave equation

NASA Astrophysics Data System (ADS)

Hu, Yanbo

2018-07-01

This paper is concerned with the degenerate initial-boundary value problem to the one-dimensional nonlinear wave equation utt =((1 + u) aux) x which arises in a number of various physical contexts. The global existence of smooth solutions to the degenerate problem was established under relaxed conditions on the initial-boundary data by the characteristic decomposition method. Moreover, we show that the solution is uniformly C 1 , α continuous up to the degenerate boundary and the degenerate curve is C 1 , α continuous for α ∈ (0 , min ⁡ a/1+a, 1/1+a).

A solution of the geodetic boundary value problem to order e3

NASA Technical Reports Server (NTRS)

Mather, R. S.

1973-01-01

A solution is obtained for the geodetic boundary value problem which defines height anomalies to + or - 5 cm, if the earth were rigid. The solution takes into account the existence of the earth's topography, together with its ellipsoidal shape and atmosphere. A relation is also established between the commonly used solution of Stokes and a development correct to order e cubed. The data requirements call for a complete definition of gravity anomalies at the surface of the earth and a knowledge of elevation characteristics at all points exterior to the geoid. In addition, spherical harmonic representations must be based on geocentric rather than geodetic latitudes.

The Kirkwood{endash}Buckingham variational method and the boundary value problems for the molecular Schr{umlt o}dinger equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pupyshev, V.I.; Scherbinin, A.V.; Stepanov, N.F.

1997-11-01

The approach based on the multiplicative form of a trial wave function within the framework of the variational method, initially proposed by Kirkwood and Buckingham, is shown to be an effective analytical tool in the quantum mechanical study of atoms and molecules. As an example, the elementary proof is given to the fact that the ground state energy of a molecular system placed into the box with walls of finite height goes to the corresponding eigenvalue of the Dirichlet boundary value problem when the height of the walls is growing up to infinity. {copyright} {ital 1997 American Institute of Physics.}

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

NASA Technical Reports Server (NTRS)

Cai, Wei; Wang, Jian-Zhong

1993-01-01

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

A numerical scheme to solve unstable boundary value problems

NASA Technical Reports Server (NTRS)

Kalnay Derivas, E.

1975-01-01

A new iterative scheme for solving boundary value problems is presented. It consists of the introduction of an artificial time dependence into a modified version of the system of equations. Then explicit forward integrations in time are followed by explicit integrations backwards in time. The method converges under much more general conditions than schemes based in forward time integrations (false transient schemes). In particular it can attain a steady state solution of an elliptical system of equations even if the solution is unstable, in which case other iterative schemes fail to converge. The simplicity of its use makes it attractive for solving large systems of nonlinear equations.

A numerical scheme for singularly perturbed reaction-diffusion problems with a negative shift via numerov method

NASA Astrophysics Data System (ADS)

Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.

2017-11-01

In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted numerical method using Numerov finite difference scheme, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.

New Nonlinear Multigrid Analysis

NASA Technical Reports Server (NTRS)

Xie, Dexuan

1996-01-01

The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.

Time as an Observable in Nonrelativistic Quantum Mechanics

NASA Technical Reports Server (NTRS)

Hahne, G. E.

2003-01-01

The argument follows from the viewpoint that quantum mechanics is taken not in the usual form involving vectors and linear operators in Hilbert spaces, but as a boundary value problem for a special class of partial differential equations-in the present work, the nonrelativistic Schrodinger equation for motion of a structureless particle in four- dimensional space-time in the presence of a potential energy distribution that can be time-as well as space-dependent. The domain of interest is taken to be one of two semi-infinite boxes, one bounded by two t=constant planes and the other by two t=constant planes. Each gives rise to a characteristic boundary value problem: one in which the initial, input values on one t=constant wall are given, with zero asymptotic wavefunction values in all spatial directions, the output being the values on the second t=constant wall; the second with certain input values given on both z=constant walls, with zero asymptotic values in all directions involving time and the other spatial coordinates, the output being the complementary values on the z=constant walls. The first problem corresponds to ordinary quantum mechanics; the second, to a fully time-dependent version of a problem normally considered only for the steady state (time-independent Schrodinger equation). The second problem is formulated in detail. A conserved indefinite metric is associated with space-like propagation, where the sign of the norm of a unidirectional state corresponds to its spatial direction of travel.

The analytical solution for drug delivery system with nonhomogeneous moving boundary condition

NASA Astrophysics Data System (ADS)

Saudi, Muhamad Hakimi; Mahali, Shalela Mohd; Harun, Fatimah Noor

2017-08-01

This paper discusses the development and the analytical solution of a mathematical model based on drug release system from a swelling delivery device. The mathematical model is represented by a one-dimensional advection-diffusion equation with nonhomogeneous moving boundary condition. The solution procedures consist of three major steps. Firstly, the application of steady state solution method, which is used to transform the nonhomogeneous moving boundary condition to homogeneous boundary condition. Secondly, the application of the Landau transformation technique that gives a significant impact in removing the advection term in the system of equation and transforming the moving boundary condition to a fixed boundary condition. Thirdly, the used of separation of variables method to find the analytical solution for the resulted initial boundary value problem. The results show that the swelling rate of delivery device and drug release rate is influenced by value of growth factor r.

OPTIMIZATION OF COUNTERCURRENT STAGED PROCESSES.

DTIC Science & Technology

CHEMICAL ENGINEERING , OPTIMIZATION), (*DISTILLATION, OPTIMIZATION), INDUSTRIAL PRODUCTION, INDUSTRIAL EQUIPMENT, MATHEMATICAL MODELS, DIFFERENCE EQUATIONS, NONLINEAR PROGRAMMING, BOUNDARY VALUE PROBLEMS, NUMERICAL INTEGRATION

Quadratic RK shooting solution for a environmental parameter prediction boundary value problem

NASA Astrophysics Data System (ADS)

Famelis, Ioannis Th.; Tsitouras, Ch.

2014-10-01

Using tools of Information Geometry, the minimum distance between two elements of a statistical manifold is defined by the corresponding geodesic, e.g. the minimum length curve that connects them. Such a curve, where the probability distribution functions in the case of our meteorological data are two parameter Weibull distributions, satisfies a 2nd order Boundary Value (BV) system. We study the numerical treatment of the resulting special quadratic form system using Shooting method. We compare the solutions of the problem when we employ a classical Singly Diagonally Implicit Runge Kutta (SDIRK) 4(3) pair of methods and a quadratic SDIRK 5(3) pair . Both pairs have the same computational costs whereas the second one attains higher order as it is specially constructed for quadratic problems.

Exact solution of two collinear cracks normal to the boundaries of a 1D layered hexagonal piezoelectric quasicrystal

NASA Astrophysics Data System (ADS)

Zhou, Y.-B.; Li, X.-F.

2018-07-01

The electroelastic problem related to two collinear cracks of equal length and normal to the boundaries of a one-dimensional hexagonal piezoelectric quasicrystal layer is analysed. By using the finite Fourier transform, a mixed boundary value problem is solved when antiplane mechanical loading and inplane electric loading are applied. The problem is reduce to triple series equations, which are then transformed to a singular integral equation. For uniform remote loading, an exact solution is obtained in closed form, and explicit expressions for the electroelastic field are determined. The intensity factors of the electroelastic field and the energy release rate at the inner and outer crack tips are given and presented graphically.

Initial boundary-value problem for the spherically symmetric Einstein equations with fluids with tangential pressure.

PubMed

Brito, Irene; Mena, Filipe C

2017-08-01

We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial space-like hypersurface with a time-like boundary, there exists a unique, local in time solution to the Einstein equations in a neighbourhood of the boundary. As an application, we consider a particular elastic fluid interior matched to a vacuum exterior.

A phase transition in the first passage of a Brownian process through a fluctuating boundary with implications for neural coding.

PubMed

Taillefumier, Thibaud; Magnasco, Marcelo O

2013-04-16

Finding the first time a fluctuating quantity reaches a given boundary is a deceptively simple-looking problem of vast practical importance in physics, biology, chemistry, neuroscience, economics, and industrial engineering. Problems in which the bound to be traversed is itself a fluctuating function of time include widely studied problems in neural coding, such as neuronal integrators with irregular inputs and internal noise. We show that the probability p(t) that a Gauss-Markov process will first exceed the boundary at time t suffers a phase transition as a function of the roughness of the boundary, as measured by its Hölder exponent H. The critical value occurs when the roughness of the boundary equals the roughness of the process, so for diffusive processes the critical value is Hc = 1/2. For smoother boundaries, H > 1/2, the probability density is a continuous function of time. For rougher boundaries, H < 1/2, the probability is concentrated on a Cantor-like set of zero measure: the probability density becomes divergent, almost everywhere either zero or infinity. The critical point Hc = 1/2 corresponds to a widely studied case in the theory of neural coding, in which the external input integrated by a model neuron is a white-noise process, as in the case of uncorrelated but precisely balanced excitatory and inhibitory inputs. We argue that this transition corresponds to a sharp boundary between rate codes, in which the neural firing probability varies smoothly, and temporal codes, in which the neuron fires at sharply defined times regardless of the intensity of internal noise.

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

2014-01-01

In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul; Don, Wai-Sun

1993-01-01

The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: (1) impose the exact boundary condition only at the end of the complete RK cycle, (2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases, results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.

Using the Hilbert uniqueness method in a reconstruction algorithm for electrical impedance tomography.

PubMed

Dai, W W; Marsili, P M; Martinez, E; Morucci, J P

1994-05-01

This paper presents a new version of the layer stripping algorithm in the sense that it works essentially by repeatedly stripping away the outermost layer of the medium after having determined the conductivity value in this layer. In order to stabilize the ill posed boundary value problem related to each layer, we base our algorithm on the Hilbert uniqueness method (HUM) and implement it with the boundary element method (BEM).

The numerical-analytical implementation of the cross-sections method to the open waveguide transition of the "horn" type

NASA Astrophysics Data System (ADS)

Divakov, Dmitriy; Malykh, Mikhail; Sevastianov, Leonid; Sevastianov, Anton; Tiutiunnik, Anastasiia

2017-04-01

In the paper we construct a method for approximate solution of the waveguide problem for guided modes of an open irregular waveguide transition. The method is based on straightening of the curved waveguide boundaries by introducing new variables and applying the Kantorovich method to the problem formulated in the new variables to get a system of ordinary second-order differential equations. In the method, the boundary conditions are formulated by analogy with the partial radiation conditions in the similar problem for closed waveguide transitions. The method is implemented in the symbolic-numeric form using the Maple computer algebra system. The coefficient matrices of the system of differential equations and boundary conditions are calculated symbolically, and then the obtained boundary-value problem is solved numerically using the finite difference method. The chosen coordinate functions of Kantorovich expansions provide good conditionality of the coefficient matrices. The numerical experiment simulating the propagation of guided modes in the open waveguide transition confirms the validity of the method proposed to solve the problem.

Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions

NASA Astrophysics Data System (ADS)

Esposito, Giampiero; Fucci, Guglielmo; Kamenshchik, Alexander Yu; Kirsten, Klaus

2005-03-01

A general method is known to exist for studying Abelian and non-Abelian gauge theories, as well as Euclidean quantum gravity, at 1-loop level on manifolds with boundary. In the latter case, boundary conditions on metric perturbations h can be chosen to be completely invariant under infinitesimal diffeomorphisms, to preserve the invariance group of the theory and BRST symmetry. In the de Donder gauge, however, the resulting boundary-value problem for the Laplace-type operator acting on h is known to be self-adjoint but not strongly elliptic. The latter is a technical condition ensuring that a unique smooth solution of the boundary-value problem exists, which implies, in turn, that the global heat-kernel asymptotics yielding 1-loop divergences and 1-loop effective action actually exists. The present paper shows that, on the Euclidean 4-ball, only the scalar part of perturbative modes for quantum gravity is affected by the lack of strong ellipticity. Further evidence for lack of strong ellipticity, from an analytic point of view, is therefore obtained. Interestingly, three sectors of the scalar-perturbation problem remain elliptic, while lack of strong ellipticity is 'confined' to the remaining fourth sector. The integral representation of the resulting ζ-function asymptotics on the Euclidean 4-ball is also obtained; this remains regular at the origin by virtue of a spectral identity here obtained for the first time.

Symmetric vibrations of a liquid in a vessel with a separator and an elastic bottom

NASA Astrophysics Data System (ADS)

Goncharov, D. A.; Pozhalostin, A. A.

2018-04-01

The paper considers the problem of small axisymmetric vibrations of an ideal fluid filling a vessel with rigid walls and an elastic bottom. The liquid is divided into two layers by an elastic septum. The elastic baffle and the vessel elastic bottom are modeled by elastic membranes. The Neumann boundary-value problem is posed for the fluid. The equations of motion of the membranes are integrated with boundary conditions.

On the solution of the Helmholtz equation on regions with corners.

PubMed

Serkh, Kirill; Rokhlin, Vladimir

2016-08-16

In this paper we solve several boundary value problems for the Helmholtz equation on polygonal domains. We observe that when the problems are formulated as the boundary integral equations of potential theory, the solutions are representable by series of appropriately chosen Bessel functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.

On the solution of the Helmholtz equation on regions with corners

PubMed Central

Serkh, Kirill; Rokhlin, Vladimir

2016-01-01

In this paper we solve several boundary value problems for the Helmholtz equation on polygonal domains. We observe that when the problems are formulated as the boundary integral equations of potential theory, the solutions are representable by series of appropriately chosen Bessel functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples. PMID:27482110

Numerical boundary condition procedures and multigrid methods; Proceedings of the Symposium, NASA Ames Research Center, Moffett Field, CA, October 19-22, 1981

NASA Technical Reports Server (NTRS)

1982-01-01

Papers presented in this volume provide an overview of recent work on numerical boundary condition procedures and multigrid methods. The topics discussed include implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows; far field boundary conditions for compressible flows; and influence of boundary approximations and conditions on finite-difference solutions. Papers are also presented on fully implicit shock tracking and on the stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes.

Estimation of Magnetic Field Growth and Construction of Adaptive Mesh in Corner Domain for the Magnetostatic Problem in Three-Dimensional Space

NASA Astrophysics Data System (ADS)

Perepelkin, Eugene; Tarelkin, Aleksandr

2018-02-01

A magnetostatics problem arises when searching for the distribution of the magnetic field generated by magnet systems of many physics research facilities, e.g., accelerators. The domain in which the boundary-value problem is solved often has a piecewise smooth boundary. In this case, numerical calculations of the problem require consideration of the solution behavior in the corner domain. In this work we obtained an upper estimation of the magnetic field growth using integral formulation of the magnetostatic problem and propose a method for condensing the differential mesh near the corner domain of the vacuum in the three-dimensional space based on this estimation.

Aerodynamics of an airfoil with a jet issuing from its surface

NASA Technical Reports Server (NTRS)

Tavella, D. A.; Karamcheti, K.

1982-01-01

A simple, two dimensional, incompressible and inviscid model for the problem posed by a two dimensional wing with a jet issuing from its lower surface is considered and a parametric analysis is carried out to observe how the aerodynamic characteristics depend on the different parameters. The mathematical problem constitutes a boundary value problem where the position of part of the boundary is not known a priori. A nonlinear optimization approach was used to solve the problem, and the analysis reveals interesting characteristics that may help to better understand the physics involved in more complex situations in connection with high lift systems.

A new approach to impulsive rendezvous near circular orbit

NASA Astrophysics Data System (ADS)

Carter, Thomas; Humi, Mayer

2012-04-01

A new approach is presented for the problem of planar optimal impulsive rendezvous of a spacecraft in an inertial frame near a circular orbit in a Newtonian gravitational field. The total characteristic velocity to be minimized is replaced by a related characteristic-value function and this related optimization problem can be solved in closed form. The solution of this problem is shown to approach the solution of the original problem in the limit as the boundary conditions approach those of a circular orbit. Using a form of primer-vector theory the problem is formulated in a way that leads to relatively easy calculation of the optimal velocity increments. A certain vector that can easily be calculated from the boundary conditions determines the number of impulses required for solution of the optimization problem and also is useful in the computation of these velocity increments. Necessary and sufficient conditions for boundary conditions to require exactly three nonsingular non-degenerate impulses for solution of the related optimal rendezvous problem, and a means of calculating these velocity increments are presented. A simple example of a three-impulse rendezvous problem is solved and the resulting trajectory is depicted. Optimal non-degenerate nonsingular two-impulse rendezvous for the related problem is found to consist of four categories of solutions depending on the four ways the primer vector locus intersects the unit circle. Necessary and sufficient conditions for each category of solutions are presented. The region of the boundary values that admit each category of solutions of the related problem are found, and in each case a closed-form solution of the optimal velocity increments is presented. Similar results are presented for the simpler optimal rendezvous that require only one-impulse. For brevity degenerate and singular solutions are not discussed in detail, but should be presented in a following study. Although this approach is thought to provide simpler computations than existing methods, its main contribution may be in establishing a new approach to the more general problem.

The Goertler vortex instability mechanism in three-dimensional boundary layers

NASA Technical Reports Server (NTRS)

Hall, P.

1984-01-01

The two dimensional boundary layer on a concave wall is centrifugally unstable with respect to vortices aligned with the basic flow for sufficiently high values of the Goertler number. However, in most situations of practical interest the basic flow is three dimensional and previous theoretical investigations do not apply. The linear stability of the flow over an infinitely long swept wall of variable curvature is considered. If there is no pressure gradient in the boundary layer the instability problem can always be related to an equivalent two dimensional calculation. However, in general, this is not the case and even for small values of the crossflow velocity field dramatic differences between the two and three dimensional problems emerge. When the size of the crossflow is further increased, the vortices in the neutral location have their axes locally perpendicular to the vortex lines of the basic flow.

Hybrid state vector methods for structural dynamic and aeroelastic boundary value problems

NASA Technical Reports Server (NTRS)

Lehman, L. L.

1982-01-01

A computational technique is developed that is suitable for performing preliminary design aeroelastic and structural dynamic analyses of large aspect ratio lifting surfaces. The method proves to be quite general and can be adapted to solving various two point boundary value problems. The solution method, which is applicable to both fixed and rotating wing configurations, is based upon a formulation of the structural equilibrium equations in terms of a hybrid state vector containing generalized force and displacement variables. A mixed variational formulation is presented that conveniently yields a useful form for these state vector differential equations. Solutions to these equations are obtained by employing an integrating matrix method. The application of an integrating matrix provides a discretization of the differential equations that only requires solutions of standard linear matrix systems. It is demonstrated that matrix partitioning can be used to reduce the order of the required solutions. Results are presented for several example problems in structural dynamics and aeroelasticity to verify the technique and to demonstrate its use. These problems examine various types of loading and boundary conditions and include aeroelastic analyses of lifting surfaces constructed from anisotropic composite materials.

Laplace Boundary-Value Problem in Paraboloidal Coordinates

ERIC Educational Resources Information Center

Duggen, L.; Willatzen, M.; Voon, L. C. Lew Yan

2012-01-01

This paper illustrates both a problem in mathematical physics, whereby the method of separation of variables, while applicable, leads to three ordinary differential equations that remain fully coupled via two separation constants and a five-term recurrence relation for series solutions, and an exactly solvable problem in electrostatics, as a…

Asymptotic expansions of solutions of the heat conduction equation in internally bounded cylindrical geometry

USGS Publications Warehouse

Ritchie, R.H.; Sakakura, A.Y.

1956-01-01

The formal solutions of problems involving transient heat conduction in infinite internally bounded cylindrical solids may be obtained by the Laplace transform method. Asymptotic series representing the solutions for large values of time are given in terms of functions related to the derivatives of the reciprocal gamma function. The results are applied to the case of the internally bounded infinite cylindrical medium with, (a) the boundary held at constant temperature; (b) with constant heat flow over the boundary; and (c) with the "radiation" boundary condition. A problem in the flow of gas through a porous medium is considered in detail.

Acoustic scattering on spheroidal shapes near boundaries

NASA Astrophysics Data System (ADS)

Miloh, Touvia

2016-11-01

A new expression for the Lamé product of prolate spheroidal wave functions is presented in terms of a distribution of multipoles along the axis of the spheroid between its foci (generalizing a corresponding theorem for spheroidal harmonics). Such an "ultimate" singularity system can be effectively used for solving various linear boundary-value problems governed by the Helmholtz equation involving prolate spheroidal bodies near planar or other boundaries. The general methodology is formally demonstrated for the axisymmetric acoustic scattering problem of a rigid (hard) spheroid placed near a hard/soft wall or inside a cylindrical duct under an axial incidence of a plane acoustic wave.

Mixed problems for the Korteweg-de Vries equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Faminskii, A V

1999-06-30

Results are established concerning the non-local solubility and wellposedness in various function spaces of the mixed problem for the Korteweg-de Vries equation u{sub t}+u{sub xxx}+au{sub x}+uu{sub x}=f(t,x) in the half-strip (0,T)x(-{infinity},0). Some a priori estimates of the solutions are obtained using a special solution J(t,x) of the linearized KdV equation of boundary potential type. Properties of J are studied which differ essentially as x{yields}+{infinity} or x{yields}-{infinity}. Application of this boundary potential enables us in particular to prove the existence of generalized solutions with non-regular boundary values.

Parallel algorithms for boundary value problems

NASA Technical Reports Server (NTRS)

Lin, Avi

1990-01-01

A general approach to solve boundary value problems numerically in a parallel environment is discussed. The basic algorithm consists of two steps: the local step where all the P available processors work in parallel, and the global step where one processor solves a tridiagonal linear system of the order P. The main advantages of this approach are two fold. First, this suggested approach is very flexible, especially in the local step and thus the algorithm can be used with any number of processors and with any of the SIMD or MIMD machines. Secondly, the communication complexity is very small and thus can be used as easily with shared memory machines. Several examples for using this strategy are discussed.

Matrix Sturm-Liouville equation with a Bessel-type singularity on a finite interval

NASA Astrophysics Data System (ADS)

Bondarenko, Natalia

2017-03-01

The matrix Sturm-Liouville equation on a finite interval with a Bessel-type singularity in the end of the interval is studied. Special fundamental systems of solutions for this equation are constructed: analytic Bessel-type solutions with the prescribed behavior at the singular point and Birkhoff-type solutions with the known asymptotics for large values of the spectral parameter. The asymptotic formulas for Stokes multipliers, connecting these two fundamental systems of solutions, are derived. We also set boundary conditions and obtain asymptotic formulas for the spectral data (the eigenvalues and the weight matrices) of the boundary value problem. Our results will be useful in the theory of direct and inverse spectral problems.

The frequency-dependent response of single aerosol particles to vapour phase oscillations and its application in measuring diffusion coefficients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Preston, Thomas C.; Davies, James F.; Wilson, Kevin R.

A new method for measuring diffusion in the condensed phase of single aerosol particles is proposed and demonstrated. The technique is based on the frequency-dependent response of a binary particle to oscillations in the vapour phase of one of its chemical components. Here, we discuss how this physical situation allows for what would typically be a non-linear boundary value problem to be approximately reduced to a linear boundary value problem. For the case of aqueous aerosol particles, we investigate the accuracy of the closed-form analytical solution to this linear problem through a comparison with the numerical solution of the fullmore » problem. Then, using experimentally measured whispering gallery modes to track the frequency-dependent response of aqueous particles to relative humidity oscillations, we determine diffusion coefficients as a function of water activity. The measured diffusion coefficients are compared to previously reported values found using the two common experiments: (i) the analysis of the sorption/desorption of water from a particle after a step-wise change to the surrounding relative humidity and (ii) the isotopic exchange of water between a particle and the vapour phase. The technique presented here has two main strengths: first, when compared to the sorption/desorption experiment, it does not require the numerical evaluation of a boundary value problem during the fitting process as a closed-form expression is available. Second, when compared to the isotope exchange experiment, it does not require the use of labeled molecules. Therefore, the frequency-dependent experiment retains the advantages of these two commonly used methods but does not suffer from their drawbacks.« less

The frequency-dependent response of single aerosol particles to vapour phase oscillations and its application in measuring diffusion coefficients

DOE PAGES

Preston, Thomas C.; Davies, James F.; Wilson, Kevin R.

2017-01-13

A new method for measuring diffusion in the condensed phase of single aerosol particles is proposed and demonstrated. The technique is based on the frequency-dependent response of a binary particle to oscillations in the vapour phase of one of its chemical components. Here, we discuss how this physical situation allows for what would typically be a non-linear boundary value problem to be approximately reduced to a linear boundary value problem. For the case of aqueous aerosol particles, we investigate the accuracy of the closed-form analytical solution to this linear problem through a comparison with the numerical solution of the fullmore » problem. Then, using experimentally measured whispering gallery modes to track the frequency-dependent response of aqueous particles to relative humidity oscillations, we determine diffusion coefficients as a function of water activity. The measured diffusion coefficients are compared to previously reported values found using the two common experiments: (i) the analysis of the sorption/desorption of water from a particle after a step-wise change to the surrounding relative humidity and (ii) the isotopic exchange of water between a particle and the vapour phase. The technique presented here has two main strengths: first, when compared to the sorption/desorption experiment, it does not require the numerical evaluation of a boundary value problem during the fitting process as a closed-form expression is available. Second, when compared to the isotope exchange experiment, it does not require the use of labeled molecules. Therefore, the frequency-dependent experiment retains the advantages of these two commonly used methods but does not suffer from their drawbacks.« less

Numerical Solution of the Electron Transport Equation in the Upper Atmosphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Woods, Mark Christopher; Holmes, Mark; Sailor, William C

A new approach for solving the electron transport equation in the upper atmosphere is derived. The problem is a very stiff boundary value problem, and to obtain an accurate numerical solution, matrix factorizations are used to decouple the fast and slow modes. A stable finite difference method is applied to each mode. This solver is applied to a simplifieed problem for which an exact solution exists using various versions of the boundary conditions that might arise in a natural auroral display. The numerical and exact solutions are found to agree with each other to at least two significant digits.

Domain identification in impedance computed tomography by spline collocation method

NASA Technical Reports Server (NTRS)

Kojima, Fumio

1990-01-01

A method for estimating an unknown domain in elliptic boundary value problems is considered. The problem is formulated as an inverse problem of integral equations of the second kind. A computational method is developed using a splice collocation scheme. The results can be applied to the inverse problem of impedance computed tomography (ICT) for image reconstruction.

Variable Viscosity Effects on Time Dependent Magnetic Nanofluid Flow past a Stretchable Rotating Plate

NASA Astrophysics Data System (ADS)

Ram, Paras; Joshi, Vimal Kumar; Sharma, Kushal; Walia, Mittu; Yadav, Nisha

2016-01-01

An attempt has been made to describe the effects of geothermal viscosity with viscous dissipation on the three dimensional time dependent boundary layer flow of magnetic nanofluids due to a stretchable rotating plate in the presence of a porous medium. The modelled governing time dependent equations are transformed a from boundary value problem to an initial value problem, and thereafter solved by a fourth order Runge-Kutta method in MATLAB with a shooting technique for the initial guess. The influences of mixed temperature, depth dependent viscosity, and the rotation strength parameter on the flow field and temperature field generated on the plate surface are investigated. The derived results show direct impact in the problems of heat transfer in high speed computer disks (Herrero et al. [1]) and turbine rotor systems (Owen and Rogers [2]).

Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities

NASA Astrophysics Data System (ADS)

Alessandrini, Giovanni; de Hoop, Maarten V.; Gaburro, Romina

2017-12-01

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body Ω\\subset{R}n when the so-called Neumann-to-Dirichlet map is locally given on a non-empty curved portion Σ of the boundary \\partialΩ . We prove that anisotropic conductivities that are a priori known to be piecewise constant matrices on a given partition of Ω with curved interfaces can be uniquely determined in the interior from the knowledge of the local Neumann-to-Dirichlet map.

A mathematical model of a steady flow through the Kaplan turbine - The existence of a weak solution in the case of an arbitrarily large inflow

NASA Astrophysics Data System (ADS)

Neustupa, Tomáš

2017-07-01

The paper presents the mathematical model of a steady 2-dimensional viscous incompressible flow through a radial blade machine. The corresponding boundary value problem is studied in the rotating frame. We provide the classical and weak formulation of the problem. Using a special form of the so called "artificial" or "natural" boundary condition on the outflow, we prove the existence of a weak solution for an arbitrarily large inflow.

Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. Part 1. Boundary Value Problems for Linear Ellilptic Equation of Second Order.

DTIC Science & Technology

1986-05-01

neighborhood of the Program PROBE of Noetic Technologies, St. Louis. corners of the domain, place where the type of the boundary condition changes, etc...is studied . , r ° -. o. - *- . ,. .- -*. ... - - . . . ’ , ..- , .- *- , . --s,." . ",-:, "j’ . ], k i-, j!3 ,, :,’ - .A L...Manual. Noetic Technologies Corp., St. Louis, Missouri (1985). 318] Szab’, B. A.: Implementation of a Finite Element Software System with h and p

Group invariant solution for a pre-existing fluid-driven fracture in impermeable rock

NASA Astrophysics Data System (ADS)

Fitt, A. D.; Mason, D. P.; Moss, E. A.

2007-11-01

The propagation of a two-dimensional fluid-driven fracture in impermeable rock is considered. The fluid flow in the fracture is laminar. By applying lubrication theory a partial differential equation relating the half-width of the fracture to the fluid pressure is derived. To close the model the PKN formulation is adopted in which the fluid pressure is proportional to the half-width of the fracture. By considering a linear combination of the Lie point symmetries of the resulting non-linear diffusion equation the boundary value problem is expressed in a form appropriate for a similarity solution. The boundary value problem is reformulated as two initial value problems which are readily solved numerically. The similarity solution describes a preexisting fracture since both the total volume and length of the fracture are initially finite and non-zero. Applications in which the rate of fluid injection into the fracture and the pressure at the fracture entry are independent of time are considered.

The Riemann-Hilbert approach to the Helmholtz equation in a quarter-plane: Neumann, Robin and Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Its, Alexander; Its, Elizabeth

2018-04-01

We revisit the Helmholtz equation in a quarter-plane in the framework of the Riemann-Hilbert approach to linear boundary value problems suggested in late 1990s by A. Fokas. We show the role of the Sommerfeld radiation condition in Fokas' scheme.

Numerical methods for incompressible viscous flows with engineering applications

NASA Technical Reports Server (NTRS)

Rose, M. E.; Ash, R. L.

1988-01-01

A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.

Acoustic-Liner Admittance in a Duct

NASA Technical Reports Server (NTRS)

Watson, W. R.

1986-01-01

Method calculates admittance from easily obtainable values. New method for calculating acoustic-liner admittance in rectangular duct with grazing flow based on finite-element discretization of acoustic field and reposing of unknown admittance value as linear eigenvalue problem on admittance value. Problem solved by Gaussian elimination. Unlike existing methods, present method extendable to mean flows with two-dimensional boundary layers as well. In presence of shear, results of method compared well with results of Runge-Kutta integration technique.

Impact and Penetration Problems.

DTIC Science & Technology

1981-03-16

constant is now determined theoretically. iii) By utilizing the formal similarity between the two criteria (1) and (3), we can predict the theoretical...cohesive strengths of various crystals. Once the experimental value for y is given, the calculations can be carried 4 out easily to determine the...analytical solution to the mixed boundary value problem yields the nonlocal displacement and stress fields. The nonlocal parameter c is determined by

Optimal trajectories based on linear equations

NASA Technical Reports Server (NTRS)

Carter, Thomas E.

1990-01-01

The Principal results of a recent theory of fuel optimal space trajectories for linear differential equations are presented. Both impulsive and bounded-thrust problems are treated. A new form of the Lawden Primer vector is found that is identical for both problems. For this reason, starting iteratives from the solution of the impulsive problem are highly effective in the solution of the two-point boundary-value problem associated with bounded thrust. These results were applied to the problem of fuel optimal maneuvers of a spacecraft near a satellite in circular orbit using the Clohessy-Wiltshire equations. For this case two-point boundary-value problems were solved using a microcomputer, and optimal trajectory shapes displayed. The results of this theory can also be applied if the satellite is in an arbitrary Keplerian orbit through the use of the Tschauner-Hempel equations. A new form of the solution of these equations has been found that is identical for elliptical, parabolic, and hyperbolic orbits except in the way that a certain integral is evaluated. For elliptical orbits this integral is evaluated through the use of the eccentric anomaly. An analogous evaluation is performed for hyperbolic orbits.

Existence and uniqueness theorems for impulsive fractional differential equations with the two-point and integral boundary conditions.

PubMed

Mardanov, M J; Mahmudov, N I; Sharifov, Y A

2014-01-01

We study a boundary value problem for the system of nonlinear impulsive fractional differential equations of order α (0 < α ≤ 1) involving the two-point and integral boundary conditions. Some new results on existence and uniqueness of a solution are established by using fixed point theorems. Some illustrative examples are also presented. We extend previous results even in the integer case α = 1.

High-order finite-volume solutions of the steady-state advection-diffusion equation with nonlinear Robin boundary conditions

NASA Astrophysics Data System (ADS)

Lin, Zhi; Zhang, Qinghai

2017-09-01

We propose high-order finite-volume schemes for numerically solving the steady-state advection-diffusion equation with nonlinear Robin boundary conditions. Although the original motivation comes from a mathematical model of blood clotting, the nonlinear boundary conditions may also apply to other scientific problems. The main contribution of this work is a generic algorithm for generating third-order, fourth-order, and even higher-order explicit ghost-filling formulas to enforce nonlinear Robin boundary conditions in multiple dimensions. Under the framework of finite volume methods, this appears to be the first algorithm of its kind. Numerical experiments on boundary value problems show that the proposed fourth-order formula can be much more accurate and efficient than a simple second-order formula. Furthermore, the proposed ghost-filling formulas may also be useful for solving other partial differential equations.

Quasi-stationary mechanics of elastic continua with bending stiffness wrapping on a pulley system

NASA Astrophysics Data System (ADS)

Kaczmarczyk, S.; Mirhadizadeh, S.

2016-05-01

In many engineering applications elastic continua such as ropes and belts often are subject to bending when they pass over pulleys / sheaves. In this paper the quasi-stationary mechanics of a cable-pulley system is studied. The cable is modelled as a moving Euler- Bernoulli beam. The distribution of tension is non-uniform along its span and due to the bending stiffness the contact points at the pulley-beam boundaries are not unknown. The system is described by a set of nonlinear ordinary differential equations with undetermined boundary conditions. The resulting nonlinear Boundary Value Problem (BVP) with unknown boundaries is solved by converting the problem into the ‘standard’ form defined over a fixed interval. Numerical results obtained for a range of typical configurations with relevant boundary conditions applied demonstrate that due to the effects of bending stiffness the angels of wrap are reduced and the span tensions are increased.

Slip Boundary Conditions for the Compressible Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Aoki, Kazuo; Baranger, Céline; Hattori, Masanari; Kosuge, Shingo; Martalò, Giorgio; Mathiaud, Julien; Mieussens, Luc

2017-11-01

The slip boundary conditions for the compressible Navier-Stokes equations are derived systematically from the Boltzmann equation on the basis of the Chapman-Enskog solution of the Boltzmann equation and the analysis of the Knudsen layer adjacent to the boundary. The resulting formulas of the slip boundary conditions are summarized with explicit values of the slip coefficients for hard-sphere molecules as well as the Bhatnagar-Gross-Krook model. These formulas, which can be applied to specific problems immediately, help to prevent the use of often used slip boundary conditions that are either incorrect or without theoretical basis.

Boundary layer and fundamental problems of hydrodynamics (compatibility of a logarithmic velocity profile in a turbulent boundary layer with the experience values)

NASA Astrophysics Data System (ADS)

Zaryankin, A. E.

2017-11-01

The compatibility of the semiempirical turbulence theory of L. Prandtl with the actual flow pattern in a turbulent boundary layer is considered in this article, and the final calculation results of the boundary layer is analyzed based on the mentioned theory. It shows that accepted additional conditions and relationships, which integrate the differential equation of L. Prandtl, associating the turbulent stresses in the boundary layer with the transverse velocity gradient, are fulfilled only in the near-wall region where the mentioned equation loses meaning and are inconsistent with the physical meaning on the main part of integration. It is noted that an introduced concept about the presence of a laminar sublayer between the wall and the turbulent boundary layer is the way of making of a physical meaning to the logarithmic velocity profile, and can be defined as adjustment of the actual flow to the formula that is inconsistent with the actual boundary conditions. It shows that coincidence of the experimental data with the actual logarithmic profile is obtained as a result of the use of not particular physical value, as an argument, but function of this value.

Versions of the collocation and least squares method for solving biharmonic equations in non-canonical domains

NASA Astrophysics Data System (ADS)

Belyaev, V. A.; Shapeev, V. P.

2017-10-01

New versions of the collocations and least squares method of high-order accuracy are proposed and implemented for the numerical solution of the boundary value problems for the biharmonic equation in non-canonical domains. The solution of the biharmonic equation is used for simulating the stress-strain state of an isotropic plate under the action of transverse load. The differential problem is projected into a space of fourth-degree polynomials by the CLS method. The boundary conditions for the approximate solution are put down exactly on the boundary of the computational domain. The versions of the CLS method are implemented on the grids which are constructed in two different ways. It is shown that the approximate solution of problems converges with high order. Thus it matches with high accuracy with the analytical solution of the test problems in the case of known solution in the numerical experiments on the convergence of the solution of various problems on a sequence of grids.

Numerical solution of the general coupled nonlinear Schrödinger equations on unbounded domains.

PubMed

Li, Hongwei; Guo, Yue

2017-12-01

The numerical solution of the general coupled nonlinear Schrödinger equations on unbounded domains is considered by applying the artificial boundary method in this paper. In order to design the local absorbing boundary conditions for the coupled nonlinear Schrödinger equations, we generalize the unified approach previously proposed [J. Zhang et al., Phys. Rev. E 78, 026709 (2008)PLEEE81539-375510.1103/PhysRevE.78.026709]. Based on the methodology underlying the unified approach, the original problem is split into two parts, linear and nonlinear terms, and we then achieve a one-way operator to approximate the linear term to make the wave out-going, and finally we combine the one-way operator with the nonlinear term to derive the local absorbing boundary conditions. Then we reduce the original problem into an initial boundary value problem on the bounded domain, which can be solved by the finite difference method. The stability of the reduced problem is also analyzed by introducing some auxiliary variables. Ample numerical examples are presented to verify the accuracy and effectiveness of our proposed method.

Hybrid Fourier pseudospectral/discontinuous Galerkin time-domain method for wave propagation

NASA Astrophysics Data System (ADS)

Pagán Muñoz, Raúl; Hornikx, Maarten

2017-11-01

The Fourier Pseudospectral time-domain (Fourier PSTD) method was shown to be an efficient way of modelling acoustic propagation problems as described by the linearized Euler equations (LEE), but is limited to real-valued frequency independent boundary conditions and predominantly staircase-like boundary shapes. This paper presents a hybrid approach to solve the LEE, coupling Fourier PSTD with a nodal Discontinuous Galerkin (DG) method. DG exhibits almost no restrictions with respect to geometrical complexity or boundary conditions. The aim of this novel method is to allow the computation of complex geometries and to be a step towards the implementation of frequency dependent boundary conditions by using the benefits of DG at the boundaries, while keeping the efficient Fourier PSTD in the bulk of the domain. The hybridization approach is based on conformal meshes to avoid spatial interpolation of the DG solutions when transferring values from DG to Fourier PSTD, while the data transfer from Fourier PSTD to DG is done utilizing spectral interpolation of the Fourier PSTD solutions. The accuracy of the hybrid approach is presented for one- and two-dimensional acoustic problems and the main sources of error are investigated. It is concluded that the hybrid methodology does not introduce significant errors compared to the Fourier PSTD stand-alone solver. An example of a cylinder scattering problem is presented and accurate results have been obtained when using the proposed approach. Finally, no instabilities were found during long-time calculation using the current hybrid methodology on a two-dimensional domain.

Variational algorithms for nonlinear smoothing applications

NASA Technical Reports Server (NTRS)

Bach, R. E., Jr.

1977-01-01

A variational approach is presented for solving a nonlinear, fixed-interval smoothing problem with application to offline processing of noisy data for trajectory reconstruction and parameter estimation. The nonlinear problem is solved as a sequence of linear two-point boundary value problems. Second-order convergence properties are demonstrated. Algorithms for both continuous and discrete versions of the problem are given, and example solutions are provided.

An eddy-viscosity treatment of the unsteady turbulent boundary layer on a flat plate in an expansion tube

NASA Technical Reports Server (NTRS)

Gupta, R. N.; Trimpi, R. L.

1974-01-01

An analysis is presented for the relaxation of a turbulent boundary layer on a semiinfinite flat plate after passage of a shock wave and a trailing driver gas-driven gas interface. The problem has special application to expansion tube flows. The flow-governing equations have been transformed into the Lamcrocco variables. The numerical results indicate that a fully turbulent boundary layer relaxes faster to the final steady-state values of heat transfer and skin-friction than a fully laminar boundary layer.

Boundary-value problem for plasma centrifuge at arbitrary magnetic Reynolds numbers

NASA Technical Reports Server (NTRS)

Wilhelm, H. E.; Hong, S. H.

1977-01-01

We solve in closed form the boundary-value problem for the partial differential equations which describe the (azimuthal) rotation velocity and induced magnetic fields in a cylindrical plasma centrifuge with ring electrodes of different radii and an external, axial magnetic field. The electric field, current density, and velocity distributions are discussed in terms of the Hartmann number H and the magnetic Reynolds number R. For small Hall coefficients, the induced magnetic field does not affect the plasma rotation. As a result of the Lorentz forces, the plasma rotates with speeds as high as 100,000 cm/sec around its axis of symmetry at typical conditions, so that the lighter (heavier) ion and atom components are enriched at (off) the center of the discharge cylinder.

A Riemann-Hilbert Approach to Complex Sharma-Tasso-Olver Equation on Half Line*

NASA Astrophysics Data System (ADS)

Zhang, Ning; Xia, Tie-Cheng; Hu, Bei-Bei

2017-11-01

In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma-Tasso-Olver (cSTO) equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann-Hilbert problem. The relevant jump matrices are explicitly given in terms of the matrix-value spectral functions spectral functions \\{a(λ ),b(λ )\\} and \\{A(λ ),B(λ )\\} , which depending on initial data {u}0(x)=u(x,0) and boundary data {g}0(y)=u(0,y), {g}1(y)={u}x(0,y), {g}2(y)={u}{xx}(0,y). These spectral functions are not independent, they satisfy a global relation.

Solutions for a Kirchhoff equation with critical Caffarelli–Kohn–Nirenberg growth and discontinuous nonlinearity

NASA Astrophysics Data System (ADS)

dos Santos, Gelson G.; Figueiredo, Giovany M.

2018-06-01

In this paper, we study the existence of nonegative solutions to a class of nonlinear boundary value problems of the Kirchhoff type. We prove existence results when the problem has discontinuous nonlinearity and critical Caffarelli-Kohn-Nirenberg growth.

Optimal Low Energy Earth-Moon Transfers

NASA Technical Reports Server (NTRS)

Griesemer, Paul Ricord; Ocampo, Cesar; Cooley, D. S.

2010-01-01

The optimality of a low-energy Earth-Moon transfer is examined for the first time using primer vector theory. An optimal control problem is formed with the following free variables: the location, time, and magnitude of the transfer insertion burn, and the transfer time. A constraint is placed on the initial state of the spacecraft to bind it to a given initial orbit around a first body, and on the final state of the spacecraft to limit its Keplerian energy with respect to a second body. Optimal transfers in the system are shown to meet certain conditions placed on the primer vector and its time derivative. A two point boundary value problem containing these necessary conditions is created for use in targeting optimal transfers. The two point boundary value problem is then applied to the ballistic lunar capture problem, and an optimal trajectory is shown. Additionally, the ballistic lunar capture trajectory is examined to determine whether one or more additional impulses may improve on the cost of the transfer.

Boundary value problems for multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.

Solving time-dependent two-dimensional eddy current problems

NASA Technical Reports Server (NTRS)

Lee, Min Eig; Hariharan, S. I.; Ida, Nathan

1988-01-01

Results of transient eddy current calculations are reported. For simplicity, a two-dimensional transverse magnetic field which is incident on an infinitely long conductor is considered. The conductor is assumed to be a good but not perfect conductor. The resulting problem is an interface initial boundary value problem with the boundary of the conductor being the interface. A finite difference method is used to march the solution explicitly in time. The method is shown. Treatment of appropriate radiation conditions is given special consideration. Results are validated with approximate analytic solutions. Two stringent test cases of high and low frequency incident waves are considered to validate the results.

A Simulation Study of the Overdetermined Geodetic Boundary Value Problem Using Collocation

DTIC Science & Technology

1989-03-01

9 APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED GEOPHYSICS LABORATORY AIR FORCE SYSTEMS COMMAND UNITED STATES AIR FORCE HANSCOM AIR FORCE BASE...linearized integral equation is obtained through an infinite system of integral equations which is solved step by step by means of Stokes’ function. The...computed. Since 9 and W = W(9) 4 are known on the boundary, then the boundary is known in the new coordinate system . The serious disadvantage of this

Neighboring extremals of dynamic optimization problems with path equality constraints

NASA Technical Reports Server (NTRS)

Lee, A. Y.

1988-01-01

Neighboring extremals of dynamic optimization problems with path equality constraints and with an unknown parameter vector are considered in this paper. With some simplifications, the problem is reduced to solving a linear, time-varying two-point boundary-value problem with integral path equality constraints. A modified backward sweep method is used to solve this problem. Two example problems are solved to illustrate the validity and usefulness of the solution technique.

Integral methods of solving boundary-value problems of nonstationary heat conduction and their comparative analysis

NASA Astrophysics Data System (ADS)

Kot, V. A.

2017-11-01

The modern state of approximate integral methods used in applications, where the processes of heat conduction and heat and mass transfer are of first importance, is considered. Integral methods have found a wide utility in different fields of knowledge: problems of heat conduction with different heat-exchange conditions, simulation of thermal protection, Stefantype problems, microwave heating of a substance, problems on a boundary layer, simulation of a fluid flow in a channel, thermal explosion, laser and plasma treatment of materials, simulation of the formation and melting of ice, inverse heat problems, temperature and thermal definition of nanoparticles and nanoliquids, and others. Moreover, polynomial solutions are of interest because the determination of a temperature (concentration) field is an intermediate stage in the mathematical description of any other process. The following main methods were investigated on the basis of the error norms: the Tsoi and Postol’nik methods, the method of integral relations, the Gudman integral method of heat balance, the improved Volkov integral method, the matched integral method, the modified Hristov method, the Mayer integral method, the Kudinov method of additional boundary conditions, the Fedorov boundary method, the method of weighted temperature function, the integral method of boundary characteristics. It was established that the two last-mentioned methods are characterized by high convergence and frequently give solutions whose accuracy is not worse that the accuracy of numerical solutions.

Computer simulation of solutions of polyharmonic equations in plane domain

NASA Astrophysics Data System (ADS)

Kazakova, A. O.

2018-05-01

A systematic study of plane problems of the theory of polyharmonic functions is presented. A method of reducing boundary problems for polyharmonic functions to the system of integral equations on the boundary of the domain is given and a numerical algorithm for simulation of solutions of this system is suggested. Particular attention is paid to the numerical solution of the main tasks when the values of the function and its derivatives are given. Test examples are considered that confirm the effectiveness and accuracy of the suggested algorithm.

Gesellschaft fuer angewandte Mathematik und Mechanik, Annual Scientific Meeting, Technische Universitaet Berlin, Berlin, West Germany, April 8-11, 1980, Reports. Parts 1 & 2

NASA Astrophysics Data System (ADS)

1981-04-01

The main topics discussed were related to nonparametric statistics, plane and antiplane states in finite elasticity, free-boundary-variational inequalities, the numerical solution of free boundary-value problems, discrete and combinatorial optimization, mathematical modelling in fluid mechanics, a survey and comparison regarding thermodynamic theories, invariant and almost invariant subspaces in linear systems with applications to disturbance isolation, nonlinear acoustics, and methods of function theory in the case of partial differential equations, giving particular attention to elliptic problems in the plane.

Solving time-dependent two-dimensional eddy current problems

NASA Technical Reports Server (NTRS)

Lee, Min Eig; Hariharan, S. I.; Ida, Nathan

1990-01-01

Transient eddy current calculations are presented for an EM wave-scattering and field-penetrating case in which a two-dimensional transverse magnetic field is incident on a good (i.e., not perfect) and infinitely long conductor. The problem thus posed is of initial boundary-value interface type, where the boundary of the conductor constitutes the interface. A potential function is used for time-domain modeling of the situation, and finite difference-time domain techniques are used to march the potential function explicitly in time. Attention is given to the case of LF radiation conditions.

The resolvent of singular integral equations. [of kernel functions in mixed boundary value problems

NASA Technical Reports Server (NTRS)

Williams, M. H.

1977-01-01

The investigation reported is concerned with the construction of the resolvent for any given kernel function. In problems with ill-behaved inhomogeneous terms as, for instance, in the aerodynamic problem of flow over a flapped airfoil, direct numerical methods become very difficult. A description is presented of a solution method by resolvent which can be employed in such problems.

Optimal ballistically captured Earth-Moon transfers

NASA Astrophysics Data System (ADS)

Ricord Griesemer, Paul; Ocampo, Cesar; Cooley, D. S.

2012-07-01

The optimality of a low-energy Earth-Moon transfer terminating in ballistic capture is examined for the first time using primer vector theory. An optimal control problem is formed with the following free variables: the location, time, and magnitude of the transfer insertion burn, and the transfer time. A constraint is placed on the initial state of the spacecraft to bind it to a given initial orbit around a first body, and on the final state of the spacecraft to limit its Keplerian energy with respect to a second body. Optimal transfers in the system are shown to meet certain conditions placed on the primer vector and its time derivative. A two point boundary value problem containing these necessary conditions is created for use in targeting optimal transfers. The two point boundary value problem is then applied to the ballistic lunar capture problem, and an optimal trajectory is shown. Additionally, the problem is then modified to fix the time of transfer, allowing for optimal multi-impulse transfers. The tradeoff between transfer time and fuel cost is shown for Earth-Moon ballistic lunar capture transfers.

A class of renormalised meshless Laplacians for boundary value problems

NASA Astrophysics Data System (ADS)

Basic, Josip; Degiuli, Nastia; Ban, Dario

2018-02-01

A meshless approach to approximating spatial derivatives on scattered point arrangements is presented in this paper. Three various derivations of approximate discrete Laplace operator formulations are produced using the Taylor series expansion and renormalised least-squares correction of the first spatial derivatives. Numerical analyses are performed for the introduced Laplacian formulations, and their convergence rate and computational efficiency are examined. The tests are conducted on regular and highly irregular scattered point arrangements. The results are compared to those obtained by the smoothed particle hydrodynamics method and the finite differences method on a regular grid. Finally, the strong form of various Poisson and diffusion equations with Dirichlet or Robin boundary conditions are solved in two and three dimensions by making use of the introduced operators in order to examine their stability and accuracy for boundary value problems. The introduced Laplacian operators perform well for highly irregular point distribution and offer adequate accuracy for mesh and mesh-free numerical methods that require frequent movement of the grid or point cloud.

Propagation of Boundary-Induced Discontinuity in Stationary Radiative Transfer

NASA Astrophysics Data System (ADS)

Kawagoe, Daisuke; Chen, I.-Kun

2018-01-01

We consider the boundary value problem of the stationary transport equation in the slab domain of general dimensions. In this paper, we discuss the relation between discontinuity of the incoming boundary data and that of the solution to the stationary transport equation. We introduce two conditions posed on the boundary data so that discontinuity of the boundary data propagates along positive characteristic lines as that of the solution to the stationary transport equation. Our analysis does not depend on the celebrated velocity averaging lemma, which is different from previous works. We also introduce an example in two dimensional case which shows that piecewise continuity of the boundary data is not a sufficient condition for the main result.

Controlling Wavebreaking in a Viscous Fluid Conduit

NASA Astrophysics Data System (ADS)

Anderson, Dalton; Maiden, Michelle; Hoefer, Mark

2015-11-01

This poster will present a new technique in the experimental investigation of dispersive hydrodynamics. In shallow water flows, internal ocean waves, superfluids, and optical media, wave breaking can be resolved by a dispersive shock wave (DSW). In this work, an experimental method to control the location of DSW formation (gradient catastrophe) is explained. The central idea is to convert an initial value problem (Riemann problem) into an equivalent boundary value problem. The system to which this technique is applied is a fluid conduit resulting from high viscosity contrast between a buoyant interior and heavier exterior fluid. The conduit cross-sectional area is modeled by a nonlinear, conservative, dispersive, third order partial differential equation. Using this model, the aim is to predict the breaking location of a DSW by controlling one boundary condition. An analytical expression for this boundary condition is derived by solving the dispersionless equation backward in time from the desired step via the method of characteristics. This is used in experiment to generate an injection rate profile for a high precision piston pump. This translates to the desired conduit shape. Varying the jump height and desired breaking location indicates good control of DSW formation. This result can be improved by deriving a conduit profile by numerical simulation of the full model equation. Controlling the breaking location of a DSW allows for the investigation of dynamics independent of the boundary. Support provided by NSF CAREER DMS-1255422 , NSF EXTREEMS.

Boundary assessment under uncertainty: A case study

USGS Publications Warehouse

Pawlowsky, V.; Olea, R.A.; Davis, J.C.

1993-01-01

Estimating certain attributes within a geological body whose exact boundary is not known presents problems because of the lack of information. Estimation may result in values that are inadmissible from a geological point of view, especially with attributes which necessarily must be zero outside the boundary, such as the thickness of the oil column outside a reservoir. A simple but effective way to define the boundary is to use indicator kriging in two steps, the first for the purpose of extrapolating control points outside the body, the second to obtain a weighting function which expresses the uncertainty attached to estimations obtained in the boundary region. ?? 1993 International Association for Mathematical Geology.

Dielectric Boundary Force in Molecular Solvation with the Poisson–Boltzmann Free Energy: A Shape Derivative Approach

PubMed Central

Li, Bo; Cheng, Xiaoliang; Zhang, Zhengfang

2013-01-01

In an implicit-solvent description of molecular solvation, the electrostatic free energy is given through the electrostatic potential. This potential solves a boundary-value problem of the Poisson–Boltzmann equation in which the dielectric coefficient changes across the solute-solvent interface—the dielectric boundary. The dielectric boundary force acting on such a boundary is the negative first variation of the electrostatic free energy with respect to the location change of the boundary. In this work, the concept of shape derivative is used to define such variations and formulas of the dielectric boundary force are derived. It is shown that such a force is always in the direction toward the charged solute molecules. PMID:24058212

A numerical study of different projection-based model reduction techniques applied to computational homogenisation

NASA Astrophysics Data System (ADS)

Soldner, Dominic; Brands, Benjamin; Zabihyan, Reza; Steinmann, Paul; Mergheim, Julia

2017-10-01

Computing the macroscopic material response of a continuum body commonly involves the formulation of a phenomenological constitutive model. However, the response is mainly influenced by the heterogeneous microstructure. Computational homogenisation can be used to determine the constitutive behaviour on the macro-scale by solving a boundary value problem at the micro-scale for every so-called macroscopic material point within a nested solution scheme. Hence, this procedure requires the repeated solution of similar microscopic boundary value problems. To reduce the computational cost, model order reduction techniques can be applied. An important aspect thereby is the robustness of the obtained reduced model. Within this study reduced-order modelling (ROM) for the geometrically nonlinear case using hyperelastic materials is applied for the boundary value problem on the micro-scale. This involves the Proper Orthogonal Decomposition (POD) for the primary unknown and hyper-reduction methods for the arising nonlinearity. Therein three methods for hyper-reduction, differing in how the nonlinearity is approximated and the subsequent projection, are compared in terms of accuracy and robustness. Introducing interpolation or Gappy-POD based approximations may not preserve the symmetry of the system tangent, rendering the widely used Galerkin projection sub-optimal. Hence, a different projection related to a Gauss-Newton scheme (Gauss-Newton with Approximated Tensors- GNAT) is favoured to obtain an optimal projection and a robust reduced model.

Inflow/Outflow Boundary Conditions with Application to FUN3D

NASA Technical Reports Server (NTRS)

Carlson, Jan-Renee

2011-01-01

Several boundary conditions that allow subsonic and supersonic flow into and out of the computational domain are discussed. These boundary conditions are demonstrated in the FUN3D computational fluid dynamics (CFD) code which solves the three-dimensional Navier-Stokes equations on unstructured computational meshes. The boundary conditions are enforced through determination of the flux contribution at the boundary to the solution residual. The boundary conditions are implemented in an implicit form where the Jacobian contribution of the boundary condition is included and is exact. All of the flows are governed by the calorically perfect gas thermodynamic equations. Three problems are used to assess these boundary conditions. Solution residual convergence to machine zero precision occurred for all cases. The converged solution boundary state is compared with the requested boundary state for several levels of mesh densities. The boundary values converged to the requested boundary condition with approximately second-order accuracy for all of the cases.

Convergence of an hp-Adaptive Finite Element Strategy in Two and Three Space-Dimensions

NASA Astrophysics Data System (ADS)

Bürg, Markus; Dörfler, Willy

2010-09-01

We show convergence of an automatic hp-adaptive refinement strategy for the finite element method on the elliptic boundary value problem. The strategy is a generalization of a refinement strategy proposed for one-dimensional situations to problems in two and three space-dimensions.

Exact solution of three-dimensional transport problems using one-dimensional models. [in semiconductor devices

NASA Technical Reports Server (NTRS)

Misiakos, K.; Lindholm, F. A.

1986-01-01

Several parameters of certain three-dimensional semiconductor devices including diodes, transistors, and solar cells can be determined without solving the actual boundary-value problem. The recombination current, transit time, and open-circuit voltage of planar diodes are emphasized here. The resulting analytical expressions enable determination of the surface recombination velocity of shallow planar diodes. The method involves introducing corresponding one-dimensional models having the same values of these parameters.

A general panel method for the analysis and design of arbitrary configurations in incompressible flows. [boundary value problem

NASA Technical Reports Server (NTRS)

Johnson, F. T.

1980-01-01

A method for solving the linear integral equations of incompressible potential flow in three dimensions is presented. Both analysis (Neumann) and design (Dirichlet) boundary conditions are treated in a unified approach to the general flow problem. The method is an influence coefficient scheme which employs source and doublet panels as boundary surfaces. Curved panels possessing singularity strengths, which vary as polynomials are used, and all influence coefficients are derived in closed form. These and other features combine to produce an efficient scheme which is not only versatile but eminently suited to the practical realities of a user-oriented environment. A wide variety of numerical results demonstrating the method is presented.

C1,1 regularity for degenerate elliptic obstacle problems

NASA Astrophysics Data System (ADS)

Daskalopoulos, Panagiota; Feehan, Paul M. N.

2016-03-01

The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate-elliptic partial differential operator, where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to the obstacle problem for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset. With the aid of weighted Sobolev spaces and weighted Hölder spaces, we establish the optimal C 1 , 1 regularity (up to the boundary of the half-plane) for solutions to obstacle problems for the elliptic Heston operator when the obstacle functions are sufficiently smooth.

Crossing and creating boundaries in healthcare innovation.

PubMed

Ingerslev, Karen

2016-06-20

Purpose - This paper reports from a qualitative case study of a change initiative undertaken in a Danish public hospital setting during national healthcare reforms. The purpose of this paper is to challenge understandings of innovations as defined by being value-adding per se. Whether the effects of attempting to innovate are positive or negative is in this paper regarded as a matter of empirical investigation. Design/methodology/approach - Narrative accounts of activities during the change initiative are analysed in order to elucidate the effects of framing the change initiative as innovation on which boundaries are created and crossed. Findings - Framing change initiatives as innovation leads to intended as well as unanticipated boundary crossings where healthcare practitioners from different organizations recognize a shared problem and task. It also leads to unintended boundary reinforcements between "us and them" that may exclude the perspectives of patients or stakeholders when confronting complex problems in healthcare. This boundary reinforcement can lead to further fragmentation of healthcare despite the stated intention to create more integrated services. Practical implications - The paper suggests that researchers as well as practitioners should not presume that intentions to innovate will by themselves enhance creativity and innovation. When analysing the intended, unintended as well as unanticipated consequences of framing change initiatives as innovation, researchers and practitioner gain nuanced knowledge about the effects of intending to innovate in complex settings such as healthcare. Originality/value - This paper suggests the need for an analytical move from studying the effects of innovation to studying the effects of framing complex problems as a call for innovation.

An efficient computer based wavelets approximation method to solve Fuzzy boundary value differential equations

NASA Astrophysics Data System (ADS)

Alam Khan, Najeeb; Razzaq, Oyoon Abdul

2016-03-01

In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.

Solving Differential Equations Using Modified Picard Iteration

ERIC Educational Resources Information Center

Robin, W. A.

2010-01-01

Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and…

Receptivity and Bypass Dynamics

NASA Technical Reports Server (NTRS)

Lasseigne, D. G.; Criminale, W. O.; Joslin, R. D.; Jackson, T. L.

1999-01-01

Problems concerning laminar-turbulent transition are addressed by solving a series of initial value problems. Solutions to the temporal, initial-value problem .with an inhomogeneous forcing term imposed upon the flow are sought. It is shown that: (1) A transient disturbance lying located outside of the boundary layer can lead to the growth of an unstable Tollmein-Schlicting wave; (2) A resonance with the continuous spectrum may provide a mechanism for bypass transition; and (3) The continuum modes of a disturbance feed directly into the Tollmein-Schlicting wave downstream through non-parallel effects.

Conformal mapping and bound states in bent waveguides

NASA Astrophysics Data System (ADS)

Sadurní, E.; Schleich, W. P.

2010-12-01

Is it possible to trap a quantum particle in an open geometry? In this work we deal with the boundary value problem of the stationary Schroedinger (or Helmholtz) equation within a waveguide with straight segments and a rectangular bending. The problem can be reduced to a one-dimensional matrix Schroedinger equation using two descriptions: oblique modes and conformal coordinates. We use a corner-corrected WKB formalism to find the energies of the one-dimensional problem. It is shown that the presence of bound states is an effect due to the boundary alone, with no classical counterpart for this geometry. The conformal description proves to be simpler, as the coupling of transversal modes is not essential in this case.

A fast approach to designing airfoils from given pressure distribution in compressible flows

NASA Technical Reports Server (NTRS)

Daripa, Prabir

1987-01-01

A new inverse method for aerodynamic design of airfols is presented for subcritical flows. The pressure distribution in this method can be prescribed as a function of the arc length of the as-yet unknown body. This inverse problem is shown to be mathematically equivalent to solving only one nonlinear boundary value problem subject to known Dirichlet data on the boundary. The solution to this problem determines the airfoil, the freestream Mach number, and the upstream flow direction. The existence of a solution to a given pressure distribution is discussed. The method is easy to implement and extremely efficient. A series of results for which comparisons are made with the known airfoils is presented.

Analysis of the stress field in a wedge using the fast expansions with pointwise determined coefficients

NASA Astrophysics Data System (ADS)

Chernyshov, A. D.; Goryainov, V. V.; Danshin, A. A.

2018-03-01

The stress problem for the elastic wedge-shaped cutter of finite dimensions with mixed boundary conditions is considered. The differential problem is reduced to the system of linear algebraic equations by applying twice the fast expansions with respect to the angular and radial coordinate. In order to determine the unknown coefficients of fast expansions, the pointwise method is utilized. The problem solution derived has explicit analytical form and it’s valid for the entire domain including its boundary. The computed profiles of the displacements and stresses in a cross-section of the cutter are provided. The stress field is investigated for various values of opening angle and cusp’s radius.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Diaz, J. I.; Henry, J.; Ramos, A. M.

We prove the approximate controllability of several nonlinear parabolic boundary-value problems by means of two different methods: the first one can be called a Cancellation method and the second one uses the Kakutani fixed-point theorem.

Flutter analysis using transversality theory

NASA Technical Reports Server (NTRS)

Afolabi, D.

1993-01-01

A new method of calculating flutter boundaries of undamped aeronautical structures is presented. The method is an application of the weak transversality theorem used in catastrophe theory. In the first instance, the flutter problem is cast in matrix form using a frequency domain method, leading to an eigenvalue matrix. The characteristic polynomial resulting from this matrix usually has a smooth dependence on the system's parameters. As these parameters change with operating conditions, certain critical values are reached at which flutter sets in. Our approach is to use the transversality theorem in locating such flutter boundaries using this criterion: at a flutter boundary, the characteristic polynomial does not intersect the axis of the abscissa transversally. Formulas for computing the flutter boundaries and flutter frequencies of structures with two degrees of freedom are presented, and extension to multi-degree of freedom systems is indicated. The formulas have obvious applications in, for instance, problems of panel flutter at supersonic Mach numbers.

Boundary condition at a two-phase interface in the lattice Boltzmann method for the convection-diffusion equation.

PubMed

Yoshida, Hiroaki; Kobayashi, Takayuki; Hayashi, Hidemitsu; Kinjo, Tomoyuki; Washizu, Hitoshi; Fukuzawa, Kenji

2014-07-01

A boundary scheme in the lattice Boltzmann method (LBM) for the convection-diffusion equation, which correctly realizes the internal boundary condition at the interface between two phases with different transport properties, is presented. The difficulty in satisfying the continuity of flux at the interface in a transient analysis, which is inherent in the conventional LBM, is overcome by modifying the collision operator and the streaming process of the LBM. An asymptotic analysis of the scheme is carried out in order to clarify the role played by the adjustable parameters involved in the scheme. As a result, the internal boundary condition is shown to be satisfied with second-order accuracy with respect to the lattice interval, if we assign appropriate values to the adjustable parameters. In addition, two specific problems are numerically analyzed, and comparison with the analytical solutions of the problems numerically validates the proposed scheme.

Laplacian versus topography in the solution of the linear gravimetric boundary value problem by means of successive approximations

NASA Astrophysics Data System (ADS)

Holota, Petr; Nesvadba, Otakar

2017-04-01

The aim of this paper is to discuss the solution of the linearized gravimetric boundary value problem by means of the method of successive approximations. We start with the relation between the geometry of the solution domain and the structure of Laplace's operator. Similarly as in other branches of engineering and mathematical physics a transformation of coordinates is used that offers a possibility to solve an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. Laplace's operator has a relatively simple structure in terms of ellipsoidal coordinates which are frequently used in geodesy. However, the physical surface of the Earth substantially differs from an oblate ellipsoid of revolution, even if it is optimally fitted. Therefore, an alternative is discussed. A system of general curvilinear coordinates such that the physical surface of the Earth is imbedded in the family of coordinate surfaces is used. Clearly, the structure of Laplace's operator is more complicated in this case. It was deduced by means of tensor calculus and in a sense it represents the topography of the physical surface of the Earth. Nevertheless, the construction of the respective Green's function is more simple, if the solution domain is transformed. This enables the use of the classical Green's function method together with the method of successive approximations for the solution of the linear gravimetric boundary value problem expressed in terms of new coordinates. The structure of iteration steps is analyzed and where useful also modified by means of the integration by parts. Comparison with other methods is discussed.

Student's Lab Assignments in PDE Course with MAPLE.

ERIC Educational Resources Information Center

Ponidi, B. Alhadi

Computer-aided software has been used intensively in many mathematics courses, especially in computational subjects, to solve initial value and boundary value problems in Partial Differential Equations (PDE). Many software packages were used in student lab assignments such as FORTRAN, PASCAL, MATLAB, MATHEMATICA, and MAPLE in order to accelerate…

A Kernel-free Boundary Integral Method for Elliptic Boundary Value Problems ⋆

PubMed Central

Ying, Wenjun; Henriquez, Craig S.

2013-01-01

This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green's functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green's functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GM-RES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong. PMID:23519600

Numerical Treatment of Degenerate Diffusion Equations via Feller's Boundary Classification, and Applications

NASA Technical Reports Server (NTRS)

Cacio, Emanuela; Cohn, Stephen E.; Spigler, Renato

2011-01-01

A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.

Solution of the modified Helmholtz equation in a triangular domain and an application to diffusion-limited coalescence.

PubMed

ben-Avraham, D; Fokas, A S

2001-07-01

A new transform method for solving boundary value problems for linear and integrable nonlinear partial differential equations recently introduced in the literature is used here to obtain the solution of the modified Helmholtz equation q(xx)(x,y)+q(yy)(x,y)-4 beta(2)q(x,y)=0 in the triangular domain 0< or =x< or =L-y< or =L, with mixed boundary conditions. This solution is applied to the problem of diffusion-limited coalescence, A+A<==>A, in the segment (-L/2,L/2), with traps at the edges.

Variational formulation for Black-Scholes equations in stochastic volatility models

NASA Astrophysics Data System (ADS)

Gyulov, Tihomir B.; Valkov, Radoslav L.

2012-11-01

In this note we prove existence and uniqueness of weak solutions to a boundary value problem arising from stochastic volatility models in financial mathematics. Our settings are variational in weighted Sobolev spaces. Nevertheless, as it will become apparent our variational formulation agrees well with the stochastic part of the problem.

An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

NASA Astrophysics Data System (ADS)

Beretta, Elena; Cavaterra, Cecilia; Cerutti, M. Cristina; Manzoni, Andrea; Ratti, Luca

2017-10-01

In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential in the myocardial tissue. The goal is the detection of an inhomogeneity \

Analysis of the Hessian for Inverse Scattering Problems. Part 1: Inverse Shape Scattering of Acoustic Waves

DTIC Science & Technology

2011-06-01

in giving us of a copy of his habilitation thesis, without which this article would not have been possible. We also thank Prof. Karsten Eppler for...John Wiley & Sons, 1983. [19] Andreas Kirsch. Generalized boundary value- and control problems for the Helmholtz equation. Habilitation thesis, 1984

Analysis of a parallelized nonlinear elliptic boundary value problem solver with application to reacting flows

NASA Technical Reports Server (NTRS)

Keyes, David E.; Smooke, Mitchell D.

1987-01-01

A parallelized finite difference code based on the Newton method for systems of nonlinear elliptic boundary value problems in two dimensions is analyzed in terms of computational complexity and parallel efficiency. An approximate cost function depending on 15 dimensionless parameters is derived for algorithms based on stripwise and boxwise decompositions of the domain and a one-to-one assignment of the strip or box subdomains to processors. The sensitivity of the cost functions to the parameters is explored in regions of parameter space corresponding to model small-order systems with inexpensive function evaluations and also a coupled system of nineteen equations with very expensive function evaluations. The algorithm was implemented on the Intel Hypercube, and some experimental results for the model problems with stripwise decompositions are presented and compared with the theory. In the context of computational combustion problems, multiprocessors of either message-passing or shared-memory type may be employed with stripwise decompositions to realize speedup of O(n), where n is mesh resolution in one direction, for reasonable n.

A three dimensional finite element formulation for thermoviscoelastic orthotropic media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zocher, M.A.

1997-12-31

A numerical algorithm for the efficient solution of the uncoupled quasistatic initial/boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and/or mechanical deformation is briefly outlined.

Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)

NASA Astrophysics Data System (ADS)

Dubinskii, Yu A.; Osipenko, A. S.

2000-02-01

Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.

Rapid optimization of multiple-burn rocket flights.

NASA Technical Reports Server (NTRS)

Brown, K. R.; Harrold, E. F.; Johnson, G. W.

1972-01-01

Different formulations of the fuel optimization problem for multiple burn trajectories are considered. It is shown that certain customary idealizing assumptions lead to an ill-posed optimization problem for which no solution exists. Several ways are discussed for avoiding such difficulties by more realistic problem statements. An iterative solution of the boundary value problem is presented together with efficient coast arc computations, the right end conditions for various orbital missions, and some test results.

Response of Non-Linear Shock Absorbers-Boundary Value Problem Analysis

NASA Astrophysics Data System (ADS)

Rahman, M. A.; Ahmed, U.; Uddin, M. S.

2013-08-01

A nonlinear boundary value problem of two degrees-of-freedom (DOF) untuned vibration damper systems using nonlinear springs and dampers has been numerically studied. As far as untuned damper is concerned, sixteen different combinations of linear and nonlinear springs and dampers have been comprehensively analyzed taking into account transient terms. For different cases, a comparative study is made for response versus time for different spring and damper types at three important frequency ratios: one at r = 1, one at r > 1 and one at r <1. The response of the system is changed because of the spring and damper nonlinearities; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. The analysis also shows that higher nonlinearity terms make the system more unstable. Numerical simulation includes transient vibrations. Although problems are much more complicated compared to those for a tuned absorber, a comparison of the results generated by the present numerical scheme with the exact one shows quite a reasonable agreement

On Stable Wall Boundary Conditions for the Hermite Discretization of the Linearised Boltzmann Equation

NASA Astrophysics Data System (ADS)

Sarna, Neeraj; Torrilhon, Manuel

2018-01-01

We define certain criteria, using the characteristic decomposition of the boundary conditions and energy estimates, which a set of stable boundary conditions for a linear initial boundary value problem, involving a symmetric hyperbolic system, must satisfy. We first use these stability criteria to show the instability of the Maxwell boundary conditions proposed by Grad (Commun Pure Appl Math 2(4):331-407, 1949). We then recognise a special block structure of the moment equations which arises due to the recursion relations and the orthogonality of the Hermite polynomials; the block structure will help us in formulating stable boundary conditions for an arbitrary order Hermite discretization of the Boltzmann equation. The formulation of stable boundary conditions relies upon an Onsager matrix which will be constructed such that the newly proposed boundary conditions stay close to the Maxwell boundary conditions at least in the lower order moments.

Analysis of 3D poroelastodynamics using BEM based on modified time-step scheme

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Petrov, A. N.; Vorobtsov, I. V.

2017-10-01

The development of 3d boundary elements modeling of dynamic partially saturated poroelastic media using a stepping scheme is presented in this paper. Boundary Element Method (BEM) in Laplace domain and the time-stepping scheme for numerical inversion of the Laplace transform are used to solve the boundary value problem. The modified stepping scheme with a varied integration step for quadrature coefficients calculation using the symmetry of the integrand function and integral formulas of Strongly Oscillating Functions was applied. The problem with force acting on a poroelastic prismatic console end was solved using the developed method. A comparison of the results obtained by the traditional stepping scheme with the solutions obtained by this modified scheme shows that the computational efficiency is better with usage of combined formulas.

Boundary-value problem for a counterrotating electrical discharge in an axial magnetic field. [plasma centrifuge for isotope separation

NASA Technical Reports Server (NTRS)

Hong, S. H.; Wilhelm, H. E.

1978-01-01

An electrical discharge between two ring electrodes embedded in the mantle of a cylindrical chamber is considered, in which the plasma in the anode and cathode regions rotates in opposite directions under the influence of an external axial magnetic field. The associated boundary-value problem for the coupled partial differential equations describing the azimuthal velocity and radial current-density fields is solved in closed form. The velocity, current density, induced magnetic induction, and electric fields are presented for typical Hartmann numbers, magnetic Reynolds numbers, and geometry parameters. The discharge is shown to produce anodic and cathodic plasma sections rotating at speeds of the order 1,000,000 cm/sec for conventional magnetic field intensities. Possible application of the magnetoactive discharge as a plasma centrifuge for isotope separation is discussed.

A multilevel correction adaptive finite element method for Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Hu, Guanghui; Xie, Hehu; Xu, Fei

2018-02-01

In this paper, an adaptive finite element method is proposed for solving Kohn-Sham equation with the multilevel correction technique. In the method, the Kohn-Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn-Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn-Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments.

Electromigration-induced void grain-boundary interactions: The mean time to failure for copper interconnects with bamboo and near-bamboo structures

NASA Astrophysics Data System (ADS)

Ogurtani, Tarik Omer; Oren, Ersin Emre

2004-12-01

A well-posed moving boundary-value problem, describing the dynamics of curved interfaces and surfaces associated with voids and/or cracks that are interacting with grain boundaries, is obtained. Extensive computer simulations are performed for void configuration evolution during intergranular motion, under the actions of capillary and electromigration forces in thin-film metallic interconnects with bamboo structures. The analysis of experimental data, utilizing the mean time to failure formulas derived in this paper, gives consistent values for the interface diffusion coefficients and enthalpies of voids. 5.85×10-5exp(-0.95eV/kT)m2s-1 is the value obtained for voids that form in the interior of the copper interconnects avoiding any surface contamination. 1.80×10-4exp(-1.20eV/kT)m2s-1 is obtained for those voids that nucleate either at triple junctions or at the grain-boundary technical surface intersections (grain-boundary groove), where the chemical impurities such as Si, O, S, and even C are segregated during the metallization and annealing processes and may act as trap centers for hopping vacancies.

On a difficulty in eigenfunction expansion solutions for the start-up of fluid flow

NASA Astrophysics Data System (ADS)

Christov, Ivan C.

2015-11-01

Most mathematics and engineering textbooks describe the process of ``subtracting off'' the steady state of a linear parabolic partial differential equation as a technique for obtaining a boundary-value problem with homogeneous boundary conditions that can be solved by separation of variables (i.e., eigenfunction expansions). While this method produces the correct solution for the start-up of the flow of, e.g., a Newtonian fluid between parallel plates, it can lead to erroneous solutions to the corresponding problem for a class of non-Newtonian fluids. We show that the reason for this is the non-rigorous enforcement of the start-up condition in the textbook approach, which leads to a violation of the principle of causality. Nevertheless, these boundary-value problems can be solved correctly using eigenfunction expansions, and we present the formulation that makes this possible (in essence, an application of Duhamel's principle). The solutions obtained by this new approach are shown to agree identically with those obtained by using the Laplace transform in time only, a technique that enforces the proper start-up condition implicitly (hence, the same error cannot be committed). Supported, in part, by NSF Grant DMS-1104047 and the U.S. DOE (Contract No. DE-AC52-06NA25396) through the LANL/LDRD Program.

Discrete shear-transformation-zone plasticity modeling of notched bars

NASA Astrophysics Data System (ADS)

Kondori, Babak; Amine Benzerga, A.; Needleman, Alan

2018-02-01

Plane strain tension analyses of un-notched and notched bars are carried out using discrete shear transformation zone plasticity. In this framework, the carriers of plastic deformation are shear transformation zones (STZs) which are modeled as Eshelby inclusions. Superposition is used to represent a boundary value problem solution in terms of discretely modeled Eshelby inclusions, given analytically for an infinite elastic medium, and an image solution that enforces the prescribed boundary conditions. The image problem is a standard linear elastic boundary value problem that is solved by the finite element method. Potential STZ activation sites are randomly distributed in the bars and constitutive relations are specified for their evolution. Results are presented for un-notched bars, for bars with blunt notches and for bars with sharp notches. The computed stress-strain curves are serrated with the magnitude of the associated stress-drops depending on bar size, notch acuity and STZ evolution. Cooperative deformation bands (shear bands) emerge upon straining and, in some cases, high stress levels occur within the bands. Effects of specimen geometry and size on the stress-strain curves are explored. Depending on STZ kinetics, notch strengthening, notch insensitivity or notch weakening are obtained. The analyses provide a rationale for some conflicting findings regarding notch effects on the mechanical response of metallic glasses.

Numerical simulation of low gravity draining. [computerized simulation of liquid sloshing in cylindrical tanks, and boundary value problems

NASA Technical Reports Server (NTRS)

Bizzell, G. D.; Crane, G. E.

1976-01-01

A boundary value problem was solved numerically for a liquid that is assumed to be inviscid and incompressible, having a motion that is irrotational and axisymmetric, and having a constant (5 degrees) solid-liquid contact angle. The avoidance of excessive mesh distortion, encountered with strictly Lagrangian or Eulerian kinematics, was achieved by introducing an auxiliary kinematic velocity field along the free surface in order to vary the trajectories used in integrating the ordinary differential equations simulating the moving boundary. The computation of the velocity potential was based upon a nonuniform triangular mesh which was automatically revised to varying depths to accommodate the motion of the free surface. These methods permitted calculation of draining induced axisymmetric slosh through the many (or fractional) finite amplitude oscillations that can occur depending upon the balance of draining, gravitational, and surface tension forces. Velocity fields, evolution of the free surface with time, and liquid residual volumes were computed for three and one half decades of Weber number and for two Bond numbers, tank fill levels, and drain radii. Comparisons with experimental data are very satisfactory.

An abstract model for radiative transfer in an atmosphere with reflection by the planetary surface

NASA Astrophysics Data System (ADS)

Greenberg, W.; van der Mee, C. V. M.

1985-07-01

A Hilbert-space model is developed that applies to radiative transfer in a homogeneous, plane-parallel planetary atmosphere. Reflection and absorption by the planetary surface are taken into account by imposing a reflective boundary condition. The existence and uniqueness of the solution of this boundary value problem are established by proving the invertibility of a scattering operator using the Fredholm alternative.

A hybrid perturbation-Galerkin method for differential equations containing a parameter

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1989-01-01

A two-step hybrid perturbation-Galerkin method to solve a variety of differential equations which involve a parameter is presented and discussed. The method consists of: (1) the use of a perturbation method to determine the asymptotic expansion of the solution about one or more values of the parameter; and (2) the use of some of the perturbation coefficient functions as trial functions in the classical Bubnov-Galerkin method. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is illustrated first with a simple linear two-point boundary value problem and is then applied to a nonlinear two-point boundary value problem in lubrication theory. The results obtained from the hybrid method are compared with approximate solutions obtained by purely numerical methods. Some general features of the method, as well as some special tips for its implementation, are discussed. A survey of some current research application areas is presented and its degree of applicability to broader problem areas is discussed.

Co-state initialization for the minimum-time low-thrust trajectory optimization

NASA Astrophysics Data System (ADS)

Taheri, Ehsan; Li, Nan I.; Kolmanovsky, Ilya

2017-05-01

This paper presents an approach for co-state initialization which is a critical step in solving minimum-time low-thrust trajectory optimization problems using indirect optimal control numerical methods. Indirect methods used in determining the optimal space trajectories typically result in two-point boundary-value problems and are solved by single- or multiple-shooting numerical methods. Accurate initialization of the co-state variables facilitates the numerical convergence of iterative boundary value problem solvers. In this paper, we propose a method which exploits the trajectory generated by the so-called pseudo-equinoctial and three-dimensional finite Fourier series shape-based methods to estimate the initial values of the co-states. The performance of the approach for two interplanetary rendezvous missions from Earth to Mars and from Earth to asteroid Dionysus is compared against three other approaches which, respectively, exploit random initialization of co-states, adjoint-control transformation and a standard genetic algorithm. The results indicate that by using our proposed approach the percent of the converged cases is higher for trajectories with higher number of revolutions while the computation time is lower. These features are advantageous for broad trajectory search in the preliminary phase of mission designs.

Multiple shooting algorithms for jump-discontinuous problems in optimal control and estimation

NASA Technical Reports Server (NTRS)

Mook, D. J.; Lew, Jiann-Shiun

1991-01-01

Multiple shooting algorithms are developed for jump-discontinuous two-point boundary value problems arising in optimal control and optimal estimation. Examples illustrating the origin of such problems are given to motivate the development of the solution algorithms. The algorithms convert the necessary conditions, consisting of differential equations and transversality conditions, into algebraic equations. The solution of the algebraic equations provides exact solutions for linear problems. The existence and uniqueness of the solution are proved.

Multispike solutions for the Brezis-Nirenberg problem in dimension three

NASA Astrophysics Data System (ADS)

Musso, Monica; Salazar, Dora

2018-06-01

We consider the problem Δu + λu +u5 = 0, u > 0, in a smooth bounded domain Ω in R3, under zero Dirichlet boundary conditions. We obtain solutions to this problem exhibiting multiple bubbling behavior at k different points of the domain as λ tends to a special positive value λ0, which we characterize in terms of the Green function of - Δ - λ.

High-Accuracy Finite Element Method: Benchmark Calculations

NASA Astrophysics Data System (ADS)

Gusev, Alexander; Vinitsky, Sergue; Chuluunbaatar, Ochbadrakh; Chuluunbaatar, Galmandakh; Gerdt, Vladimir; Derbov, Vladimir; Góźdź, Andrzej; Krassovitskiy, Pavel

2018-02-01

We describe a new high-accuracy finite element scheme with simplex elements for solving the elliptic boundary-value problems and show its efficiency on benchmark solutions of the Helmholtz equation for the triangle membrane and hypercube.

Absorbing boundary conditions for second-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Jiang, Hong; Wong, Yau Shu

1989-01-01

A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.

A two-dimensional MHD global coronal model - Steady-state streamers

NASA Technical Reports Server (NTRS)

Wang, A.-H.; Wu, S. T.; Suess, S. T.; Poletto, G.

1992-01-01

A 2D, time-dependent, numerical, MHD model for the simulation of coronal streamers from the solar surface to 15 solar is presented. Three examples are given; for dipole, quadrupole and hexapole (Legendre polynomials P1, P2, and P3) initial field topologies. The computed properties are density, temperature, velocity, and magnetic field. The calculation is set up as an initial-boundary value problem wherein a relaxation in time produces the steady state solution. In addition to the properties of the solutions, their accuracy is discussed. Besides solutions for dipole, quadrupole, and hexapole geometries, the model use of realistic values for the density and Alfven speed while still meeting the requirement that the flow speed be super-Alfvenic at the outer boundary by extending the outer boundary to 15 solar radii.

General Solutions for Hydromagnetic Free Convection Flow over an Infinite Plate with Newtonian Heating, Mass Diffusion and Chemical Reaction

NASA Astrophysics Data System (ADS)

Fetecau, Constatin; Shah, Nehad Ali; Vieru, Dumitru

2017-12-01

The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined. Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration, three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution (the steady-state), for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter.

The analytical solution of the problem of a shock focusing in a gas for one-dimensional case

NASA Astrophysics Data System (ADS)

Shestakovskaya, E. S.; Magazov, F. G.

2018-03-01

The analytical solution of the problem of an imploding shock wave in the vessel with an impermeable wall is constructed for the cases of planar, cylindrical and spherical symmetry. The negative velocity is set at the vessel boundary. The velocity of cold ideal gas is zero. At the initial time the shock spreads from this point into the center of symmetry. The boundary moves under the particular law which conforms to the movement of the shock. In Euler variables it moves but in Lagrangian variables its trajectory is a vertical line. Equations that determine the structure of the gas flow between the shock front and the boundary as a function of time and the Lagrangian coordinate as well as the dependence of the entropy on the shock wave velocity are obtained. Self-similar coefficients and corresponding critical values of self-similar coordinates were found for a wide range of adiabatic index. The problem is solved for Lagrangian coordinates.

Survey of the status of finite element methods for partial differential equations

NASA Technical Reports Server (NTRS)

Temam, Roger

1986-01-01

The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.

Collocation for an integral equation arising in duct acoustics

NASA Technical Reports Server (NTRS)

Moss, W. F.

1986-01-01

A mathematical model is developed to describe the effect of aircraft-engine inlet geometry on the reflected and radiated acoustic field without flow, as studied experimentally using a spinning-mode synthesizer by Silcox (1983). The acoustic pressure in the inlet interior and exterior is modeled by a pure cylindrical azimuthal mode for the Helmholtz equation with hardwall boundary and by the Helmholtz equation and the radiation condition at infinity, respectively. The analytical approach to the solution of the resulting boundary-value problem and the program implementation are explained; numerical results are presented in tables and graphs; and the uniqueness of the problem is demonstrated.

Unification of Intercontinental Height Systems based on the Fixed Geodetic Boundary Value Problem - A Case Study in Spherical Approximation

NASA Astrophysics Data System (ADS)

Grombein, T.; Seitz, K.; Heck, B.

2013-12-01

In general, national height reference systems are related to individual vertical datums defined by specific tide gauges. The discrepancy of these vertical datums causes height system biases that range in an order of 1-2 m at a global scale. Continental height systems can be connected by spirit leveling and gravity measurements along the leveling lines as performed for the definition of the European Vertical Reference Frame. In order to unify intercontinental height systems, an indirect connection is needed. For this purpose, global geopotential models derived from recent satellite missions like GOCE provide an important contribution. However, to achieve a highly-precise solution, a combination with local terrestrial gravity data is indispensable. Such combinations result in the solution of a Geodetic Boundary Value Problem (GBVP). In contrast to previous studies, mostly related to the traditional (scalar) free GBVP, the present paper discusses the use of the fixed GBVP for height system unification, where gravity disturbances instead of gravity anomalies are applied as boundary values. The basic idea of our approach is a conversion of measured gravity anomalies to gravity disturbances, where unknown datum parameters occur that can be associated with height system biases. In this way, the fixed GBVP can be extended by datum parameters for each datum zone. By evaluating the GBVP at GNSS/leveling benchmarks, the unknown datum parameters can be estimated in a least squares adjustment. Beside the developed theory, we present numerical results of a case study based on the spherical fixed GBVP and boundary values simulated by the use of the global geopotential model EGM2008. In a further step, the impact of approximations like linearization as well as topographic and ellipsoidal effects is taken into account by suitable reduction and correction terms.

Unified anomaly suppression and boundary extraction in laser radar range imagery based on a joint curve-evolution and expectation-maximization algorithm.

PubMed

Feng, Haihua; Karl, William Clem; Castañon, David A

2008-05-01

In this paper, we develop a new unified approach for laser radar range anomaly suppression, range profiling, and segmentation. This approach combines an object-based hybrid scene model for representing the range distribution of the field and a statistical mixture model for the range data measurement noise. The image segmentation problem is formulated as a minimization problem which jointly estimates the target boundary together with the target region range variation and background range variation directly from the noisy and anomaly-filled range data. This formulation allows direct incorporation of prior information concerning the target boundary, target ranges, and background ranges into an optimal reconstruction process. Curve evolution techniques and a generalized expectation-maximization algorithm are jointly employed as an efficient solver for minimizing the objective energy, resulting in a coupled pair of object and intensity optimization tasks. The method directly and optimally extracts the target boundary, avoiding a suboptimal two-step process involving image smoothing followed by boundary extraction. Experiments are presented demonstrating that the proposed approach is robust to anomalous pixels (missing data) and capable of producing accurate estimation of the target boundary and range values from noisy data.

Bubble contraction in free-boundary Hele-Shaw flow with surface tension and kinetic undercooling regularisation

NASA Astrophysics Data System (ADS)

Dallaston, Michael; McCue, Scott

2012-11-01

When an inviscid bubble expands into a viscous fluid in a Hele-Shaw cell, the bubble boundary is unstable, in general forming long fingers (the Saffman-Taylor instability). In order to make the problem well-posed, a regularising boundary effect must be included. The most widely studied of these are surface tension, which penalises high curvatures, and kinetic undercooling, which penalises high velocities. Both these effects act as a stabilising influence on the free boundary. Less attention has been paid to the case of contracting bubbles, which shrink to a single point (or points) in finite time. In this case, the two effects are in competition, as surface tension stabilises the boundary, while kinetic undercooling destabilises it. This leads to bifurcation behaviour in the asymptotic (near-extinction) shape of the bubble as the relative strengths of the two effects are varied. In particular, there is a critical range of parameter values for which both circular and slit-type bubbles are stable, with a third (unstable) oval-type shape also present. We discuss some numerical and analytic techniques for solving the full free boundary problem and for exploring this interesting extinction behaviour.

The Bloch Approximation in Periodically Perforated Media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Conca, C.; Gomez, D., E-mail: gomezdel@unican.es; Lobo, M.

2005-06-15

We consider a periodically heterogeneous and perforated medium filling an open domain {omega} of R{sup N}. Assuming that the size of the periodicity of the structure and of the holes is O({epsilon}),we study the asymptotic behavior, as {epsilon} {sup {yields}} 0, of the solution of an elliptic boundary value problem with strongly oscillating coefficients posed in {omega}{sup {epsilon}}({omega}{sup {epsilon}} being {omega} minus the holes) with a Neumann condition on the boundary of the holes. We use Bloch wave decomposition to introduce an approximation of the solution in the energy norm which can be computed from the homogenized solution and themore » first Bloch eigenfunction. We first consider the case where {omega}is R{sup N} and then localize the problem for abounded domain {omega}, considering a homogeneous Dirichlet condition on the boundary of {omega}.« less

Similar solutions for viscous hypersonic flow over a slender three-fourths-power body of revolution

NASA Technical Reports Server (NTRS)

Lin, Chin-Shun

1987-01-01

For hypersonic flow with a shock wave, there is a similar solution consistent throughout the viscous and inviscid layers along a very slender three-fourths-power body of revolution The strong pressure interaction problem can then be treated by the method of similarity. Numerical calculations are performed in the viscous region with the edge pressure distribution known from the inviscid similar solutions. The compressible laminar boundary-layer equations are transformed into a system of ordinary differential equations. The resulting two-point boundary value problem is then solved by the Runge-Kutta method with a modified Newton's method for the corresponding boundary conditions. The effects of wall temperature, mass bleeding, and body transverse curvature are investigated. The induced pressure, displacement thickness, skin friction, and heat transfer due to the previously mentioned parameters are estimated and analyzed.

Application of ANNs approach for wave-like and heat-like equations

NASA Astrophysics Data System (ADS)

Jafarian, Ahmad; Baleanu, Dumitru

2017-12-01

Artificial neural networks are data processing systems which originate from human brain tissue studies. The remarkable abilities of these networks help us to derive desired results from complicated raw data. In this study, we intend to duplicate an efficient iterative method to the numerical solution of two famous partial differential equations, namely the wave-like and heat-like problems. It should be noted that many physical phenomena such as coupling currents in a flat multi-strand two-layer super conducting cable, non-homogeneous elastic waves in soils and earthquake stresses, are described by initial-boundary value wave and heat partial differential equations with variable coefficients. To the numerical solution of these equations, a combination of the power series method and artificial neural networks approach, is used to seek an appropriate bivariate polynomial solution of the mentioned initial-boundary value problem. Finally, several computer simulations confirmed the theoretical results and demonstrating applicability of the method.

Existence and stability of periodic solutions of quasi-linear Korteweg — de Vries equation

NASA Astrophysics Data System (ADS)

Glyzin, S. D.; Kolesov, A. Yu; Preobrazhenskaia, M. M.

2017-01-01

We consider the scalar nonlinear differential-difference equation with two delays, which models electrical activity of a neuron. Under some additional suppositions for this equation well known method of quasi-normal forms can be applied. Its essence lies in the formal normalization of the Poincare - Dulac obtaining quasi-normal form and the subsequent application of the theorems of conformity. In this case, the result of the application of quasi-normal forms is a countable system of differential-difference equations, which can be turned into a boundary value problem of the Korteweg - de Vries equation. The investigation of this boundary value problem allows us to draw a conclusion about the behaviour of the original equation. Namely, for a suitable choice of parameters in the framework of this equation is implemented buffer phenomenon consisting in the presence of the bifurcation mechanism for the birth of an arbitrarily large number of stable cycles.

New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems

PubMed Central

Abd-Elhameed, W. M.

2014-01-01

This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases. Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced. As an application, and with the aid of the new introduced derivatives formulae, an algorithm for solving special sixth-order boundary value problems are implemented with the aid of applying Galerkin method. A numerical example is presented hoping to ascertain the validity and the applicability of the proposed algorithms. PMID:25386599

Launch flexibility using NLP guidance and remote wind sensing

NASA Technical Reports Server (NTRS)

Cramer, Evin J.; Bradt, Jerre E.; Hardtla, John W.

1990-01-01

This paper examines the use of lidar wind measurements in the implementation of a guidance strategy for a nonlinear programming (NLP) launch guidance algorithm. The NLP algorithm uses B-spline command function representation for flexibility in the design of the guidance steering commands. Using this algorithm, the guidance system solves a two-point boundary value problem at each guidance update. The specification of different boundary value problems at each guidance update provides flexibility that can be used in the design of the guidance strategy. The algorithm can use lidar wind measurements for on pad guidance retargeting and for load limiting guidance steering commands. Examples presented in the paper use simulated wind updates to correct wind induced final orbit errors and to adjust the guidance steering commands to limit the product of the dynamic pressure and angle-of-attack for launch vehicle load alleviation.

A wideband FMBEM for 2D acoustic design sensitivity analysis based on direct differentiation method

NASA Astrophysics Data System (ADS)

Chen, Leilei; Zheng, Changjun; Chen, Haibo

2013-09-01

This paper presents a wideband fast multipole boundary element method (FMBEM) for two dimensional acoustic design sensitivity analysis based on the direct differentiation method. The wideband fast multipole method (FMM) formed by combining the original FMM and the diagonal form FMM is used to accelerate the matrix-vector products in the boundary element analysis. The Burton-Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The strongly singular and hypersingular integrals in the sensitivity equations can be evaluated explicitly and directly by using the piecewise constant discretization. The iterative solver GMRES is applied to accelerate the solution of the linear system of equations. A set of optimal parameters for the wideband FMBEM design sensitivity analysis are obtained by observing the performances of the wideband FMM algorithm in terms of computing time and memory usage. Numerical examples are presented to demonstrate the efficiency and validity of the proposed algorithm.

Identification of the Thermal Conductivity Coefficient for Quasi-Stationary Two-Dimensional Heat Conduction Equations

NASA Astrophysics Data System (ADS)

Matsevityi, Yu. M.; Alekhina, S. V.; Borukhov, V. T.; Zayats, G. M.; Kostikov, A. O.

2017-11-01

The problem of identifying the time-dependent thermal conductivity coefficient in the initial-boundary-value problem for the quasi-stationary two-dimensional heat conduction equation in a bounded cylinder is considered. It is assumed that the temperature field in the cylinder is independent of the angular coordinate. To solve the given problem, which is related to a class of inverse problems, a mathematical approach based on the method of conjugate gradients in a functional form is being developed.

Anomaly formulas for the complex-valued analytic torsion on compact bordisms

PubMed Central

Maldonado Molina, Osmar

2013-01-01

We extend the complex-valued analytic torsion, introduced by Burghelea and Haller on closed manifolds, to compact Riemannian bordisms. We do so by considering a flat complex vector bundle over a compact Riemannian manifold, endowed with a fiberwise nondegenerate symmetric bilinear form. The Riemmanian metric and the bilinear form are used to define non-selfadjoint Laplacians acting on vector-valued smooth forms under absolute and relative boundary conditions. In order to define the complex-valued analytic torsion in this situation, we study spectral properties of these generalized Laplacians. Then, as main results, we obtain so-called anomaly formulas for this torsion. Our reasoning takes into account that the coefficients in the heat trace asymptotic expansion associated to the boundary value problem under consideration, are locally computable. The anomaly formulas for the complex-valued Ray–Singer torsion are derived first by using the corresponding ones for the Ray–Singer metric, obtained by Brüning and Ma on manifolds with boundary, and then an argument of analytic continuation. In odd dimensions, our anomaly formulas are in accord with the corresponding results of Su, without requiring the variations of the Riemannian metric and bilinear structures to be supported in the interior of the manifold. PMID:27087744

Generalized Forchheimer Flows of Isentropic Gases

NASA Astrophysics Data System (ADS)

Celik, Emine; Hoang, Luan; Kieu, Thinh

2018-03-01

We consider generalized Forchheimer flows of either isentropic gases or slightly compressible fluids in porous media. By using Muskat's and Ward's general form of the Forchheimer equations, we describe the fluid dynamics by a doubly nonlinear parabolic equation for the appropriately defined pseudo-pressure. The volumetric flux boundary condition is converted to a time-dependent Robin-type boundary condition for this pseudo-pressure. We study the corresponding initial boundary value problem, and estimate the L^∞ and W^{1,2-a} (with 0

Potential-splitting approach applied to the Temkin-Poet model for electron scattering off the hydrogen atom and the helium ion

NASA Astrophysics Data System (ADS)

Yarevsky, E.; Yakovlev, S. L.; Larson, Å; Elander, N.

2015-06-01

The study of scattering processes in few body systems is a difficult problem especially if long range interactions are involved. In order to solve such problems, we develop here a potential-splitting approach for three-body systems. This approach is based on splitting the reaction potential into a finite range core part and a long range tail part. The solution to the Schrödinger equation for the long range tail Hamiltonian is found analytically, and used as an incoming wave in the three body scattering problem. This reformulation of the scattering problem makes it suitable for treatment by the exterior complex scaling technique in the sense that the problem after the complex dilation is reduced to a boundary value problem with zero boundary conditions. We illustrate the method with calculations on the electron scattering off the hydrogen atom and the positive helium ion in the frame of the Temkin-Poet model.

Summation by parts, projections, and stability

NASA Technical Reports Server (NTRS)

Olsson, Pelle

1993-01-01

We have derived stability results for high-order finite difference approximations of mixed hyperbolic-parabolic initial-boundary value problems (IBVP). The results are obtained using summation by parts and a new way of representing general linear boundary conditions as an orthogonal projection. By slightly rearranging the analytic equations, we can prove strict stability for hyperbolic-parabolic IBVP. Furthermore, we generalize our technique so as to yield strict stability on curvilinear non-smooth domains in two space dimensions. Finally, we show how to incorporate inhomogeneous boundary data while retaining strict stability. Using the same procedure one can prove strict stability in higher dimensions as well.

Rotationally symmetric viscous gas flows

NASA Astrophysics Data System (ADS)

Weigant, W.; Plotnikov, P. I.

2017-03-01

The Dirichlet boundary value problem for the Navier-Stokes equations of a barotropic viscous compressible fluid is considered. The flow region and the data of the problem are assumed to be invariant under rotations about a fixed axis. The existence of rotationally symmetric weak solutions for all adiabatic exponents from the interval (γ*,∞) with a critical exponent γ* < 4/3 is proved.

A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

PubMed

Biala, T A; Jator, S N

2015-01-01

In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

On some properties of force-free magnetic fields in infinite regions of space

NASA Technical Reports Server (NTRS)

Aly, J. J.

1984-01-01

Techniques for solving boundary value problems (BVP) for a force free magnetic field (FFF) in infinite space are presented. A priori inequalities are defined which must be satisfied by the force-free equations. It is shown that upper bounds may be calculated for the magnetic energy of the region provided the value of the magnetic normal component at the boundary of the region can be shown to decay sufficiently fast at infinity. The results are employed to prove a nonexistence theorem for the BVP for the FFF in the spatial region. The implications of the theory for modeling the origins of solar flares are discussed.

Design and Experimental Implementation of Optimal Spacecraft Antenna Slews

DTIC Science & Technology

2013-12-01

LINK PENDULUM MODEL ............................................................58  C.  AZIMUTH-ELEVATION SYSTEM...BOUNDARY VALUE PROBLEM ......................77  B.  DOUBLE PENDULUM EXAMPLE............................................................82  C.  SOLVING THE...Figure 15.  Two-link Pendulum .........................................................................................58  Figure 16.  Double

Correction of Excessive Precipitation over Steep Mountains in a General Circulation Model (GCM)

NASA Technical Reports Server (NTRS)

Chao, Winston C.

2012-01-01

Excessive precipitation over steep and high mountains (EPSM) is a well-known problem in GCMs and regional climate models even at a resolution as high as 19km. The affected regions include the Andes, the Himalayas, Sierra Madre, New Guinea and others. This problem also shows up in some data assimilation products. Among the possible causes investigated in this study, we found that the most important one, by far, is a missing upward transport of heat out of the boundary layer due to the vertical circulations forced by the daytime subgrid-scale upslope winds, which in turn is forced by heated boundary layer on the slopes. These upslope winds are associated with large subgrid-scale topographic variance, which is found over steep mountains. Without such subgrid-scale heat ventilation, the resolvable-scale upslope flow in the boundary layer generated by surface sensible heat flux along the mountain slopes is excessive. Such an excessive resolvable-scale upslope flow in the boundary layer combined with the high moisture content in the boundary layer results in excessive moisture transport toward mountaintops, which in turn gives rise to excessive precipitation over the affected regions. We have parameterized the effects of subgrid-scale heated-slope-induced vertical circulation (SHVC) by removing heat from the boundary layer and depositing it in the layers higher up when topographic variance exceeds a critical value. Test results using NASA/Goddard's GEOS-5 GCM have shown that the EPSM problem is largely solved.

A numerical technique for linear elliptic partial differential equations in polygonal domains.

PubMed

Hashemzadeh, P; Fokas, A S; Smitheman, S A

2015-03-08

Integral representations for the solution of linear elliptic partial differential equations (PDEs) can be obtained using Green's theorem. However, these representations involve both the Dirichlet and the Neumann values on the boundary, and for a well-posed boundary-value problem (BVPs) one of these functions is unknown. A new transform method for solving BVPs for linear and integrable nonlinear PDEs usually referred to as the unified transform ( or the Fokas transform ) was introduced by the second author in the late Nineties. For linear elliptic PDEs, this method can be considered as the analogue of Green's function approach but now it is formulated in the complex Fourier plane instead of the physical plane. It employs two global relations also formulated in the Fourier plane which couple the Dirichlet and the Neumann boundary values. These relations can be used to characterize the unknown boundary values in terms of the given boundary data, yielding an elegant approach for determining the Dirichlet to Neumann map . The numerical implementation of the unified transform can be considered as the counterpart in the Fourier plane of the well-known boundary integral method which is formulated in the physical plane. For this implementation, one must choose (i) a suitable basis for expanding the unknown functions and (ii) an appropriate set of complex values, which we refer to as collocation points, at which to evaluate the global relations. Here, by employing a variety of examples we present simple guidelines of how the above choices can be made. Furthermore, we provide concrete rules for choosing the collocation points so that the condition number of the matrix of the associated linear system remains low.

Completed Beltrami-Michell Formulation in Polar Coordinates

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Hopkins, Dale A.

2005-01-01

A set of conditions had not been formulated on the boundary of an elastic continuum since the time of Saint-Venant. This limitation prevented the formulation of a direct stress calculation method in elasticity for a continuum with a displacement boundary condition. The missed condition, referred to as the boundary compatibility condition, is now formulated in polar coordinates. The augmentation of the new condition completes the Beltrami-Michell formulation in polar coordinates. The completed formulation that includes equilibrium equations and a compatibility condition in the field as well as the traction and boundary compatibility condition is derived from the stationary condition of the variational functional of the integrated force method. The new method is illustrated by solving an example of a mixed boundary value problem for mechanical as well as thermal loads.

The NURBS curves in modelling the shape of the boundary in the parametric integral equations systems for solving the Laplace equation

NASA Astrophysics Data System (ADS)

Zieniuk, Eugeniusz; Kapturczak, Marta; Sawicki, Dominik

2016-06-01

In solving of boundary value problems the shapes of the boundary can be modelled by the curves widely used in computer graphics. In parametric integral equations system (PIES) such curves are directly included into the mathematical formalism. Its simplify the way of definition and modification of the shape of the boundary. Until now in PIES the B-spline, Bézier and Hermite curves were used. Recent developments in the computer graphics paid our attention, therefore we implemented in PIES possibility of defining the shape of boundary using the NURBS curves. The curves will allow us to modeling different shapes more precisely. In this paper we will compare PIES solutions (with applied NURBS) with the solutions existing in the literature.

Speed selection for traveling-wave solutions to the diffusion-reaction equation with cubic reaction term and Burgers nonlinear convection.

PubMed

Sabelnikov, V A; Lipatnikov, A N

2014-09-01

The problem of traveling wave (TW) speed selection for solutions to a generalized Murray-Burgers-KPP-Fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results. Depending on the magnitude of a parameter inherent in the reaction term (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solution occurs due to interplay of two nonlinear terms; the reaction term and the Burgers convection term. Explicit pushed TW solutions are derived. It is shown that physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, can be determined by seeking the TW solution characterized by the maximum decay rate at its leading edge. In the Appendix, the developed approach is applied to a non-linear diffusion-reaction equation that is widely used to model premixed turbulent combustion.

Exact Solution to Stationary Onset of Convection Due to Surface Tension Variation in a Multicomponent Fluid Layer With Interfacial Deformation

NASA Technical Reports Server (NTRS)

Skarda, J. Raymond Lee; McCaughan, Frances E.

1998-01-01

Stationary onset of convection due to surface tension variation in an unbounded multicomponent fluid layer is considered. Surface deformation is included and general flux boundary conditions are imposed on the stratifying agencies (temperature/composition) disturbance equations. Exact solutions are obtained to the general N-component problem for both finite and infinitesimal wavenumbers. Long wavelength instability may coexist with a finite wavelength instability for certain sets of parameter values, often referred to as frontier points. For an impermeable/insulated upper boundary and a permeable/conductive lower boundary, frontier boundaries are computed in the space of Bond number, Bo, versus Crispation number, Cr, over the range 5 x 10(exp -7) less than or equal to Bo less than or equal to 1. The loci of frontier points in (Bo, Cr) space for different values of N, diffusivity ratios, and, Marangoni numbers, collapsed to a single curve in (Bo, D(dimensional variable)Cr) space, where D(dimensional variable) is a Marangoni number weighted diffusivity ratio.

Numerical simulation of vortical ideal fluid flow through curved channel

NASA Astrophysics Data System (ADS)

Moshkin, N. P.; Mounnamprang, P.

2003-04-01

A numerical algorithm to study the boundary-value problem in which the governing equations are the steady Euler equations and the vorticity is given on the inflow parts of the domain boundary is developed. The Euler equations are implemented in terms of the stream function and vorticity. An irregular physical domain is transformed into a rectangle in the computational domain and the Euler equations are rewritten with respect to a curvilinear co-ordinate system. The convergence of the finite-difference equations to the exact solution is shown experimentally for the test problems by comparing the computational results with the exact solutions on the sequence of grids. To find the pressure from the known vorticity and stream function, the Euler equations are utilized in the Gromeka-Lamb form. The numerical algorithm is illustrated with several examples of steady flow through a two-dimensional channel with curved walls. The analysis of calculations shows strong dependence of the pressure field on the vorticity given at the inflow parts of the boundary. Plots of the flow structure and isobars, for different geometries of channel and for different values of vorticity on entrance, are also presented.

A new non-iterative reconstruction method for the electrical impedance tomography problem

NASA Astrophysics Data System (ADS)

Ferreira, A. D.; Novotny, A. A.

2017-03-01

The electrical impedance tomography (EIT) problem consists in determining the distribution of the electrical conductivity of a medium subject to a set of current fluxes, from measurements of the corresponding electrical potentials on its boundary. EIT is probably the most studied inverse problem since the fundamental works by Calderón from the 1980s. It has many relevant applications in medicine (detection of tumors), geophysics (localization of mineral deposits) and engineering (detection of corrosion in structures). In this work, we are interested in reconstructing a number of anomalies with different electrical conductivity from the background. Since the EIT problem is written in the form of an overdetermined boundary value problem, the idea is to rewrite it as a topology optimization problem. In particular, a shape functional measuring the misfit between the boundary measurements and the electrical potentials obtained from the model is minimized with respect to a set of ball-shaped anomalies by using the concept of topological derivatives. It means that the objective functional is expanded and then truncated up to the second order term, leading to a quadratic and strictly convex form with respect to the parameters under consideration. Thus, a trivial optimization step leads to a non-iterative second order reconstruction algorithm. As a result, the reconstruction process becomes very robust with respect to noisy data and independent of any initial guess. Finally, in order to show the effectiveness of the devised reconstruction algorithm, some numerical experiments into two spatial dimensions are presented, taking into account total and partial boundary measurements.

A hybrid-perturbation-Galerkin technique which combines multiple expansions

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1989-01-01

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Improving a complex finite-difference ground water flow model through the use of an analytic element screening model

USGS Publications Warehouse

Hunt, R.J.; Anderson, M.P.; Kelson, V.A.

1998-01-01

This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.

A numerical analysis for non-linear radiation in MHD flow around a cylindrical surface with chemically reactive species

NASA Astrophysics Data System (ADS)

Khan, Junaid Ahmad; Mustafa, M.

2018-03-01

Boundary layer flow around a stretchable rough cylinder is modeled by taking into account boundary slip and transverse magnetic field effects. The main concern is to resolve heat/mass transfer problem considering non-linear radiative heat transfer and temperature/concentration jump aspects. Using conventional similarity approach, the equations of motion and heat transfer are converted into a boundary value problem whose solution is computed by shooting method for broad range of slip coefficients. The proposed numerical scheme appears to improve as the strengths of magnetic field and slip coefficients are enhanced. Axial velocity and temperature are considerably influenced by a parameter M which is inversely proportional to the radius of cylinder. A significant change in temperature profile is depicted for growing wall to ambient temperature ratio. Relevant physical quantities such as wall shear stress, local Nusselt number and local Sherwood number are elucidated in detail.

To problem of the definition of the boundary surface of confidence regions in non-linear case. (Russian Title: К задаче определения граничной поверхности доверительной области в нелинейном случае)

NASA Astrophysics Data System (ADS)

Syusina, O. M.; Chernitsov, A. M.; Tamarov, V. A.

2011-07-01

The method for construction of the confidence region of the motion of the small bodies of Solar system by force of defini-tion region their boundary surface in nonlinear case is proposed. In this method representation on to boundary surface of the re-gion, which obtained of nonlinear method of multiple solution of least squares problem, is realized by values of target function in vertex of confidence ellipsoid with eliminating of anomalous ones.

Numerical solution of the nonlinear Schrodinger equation by feedforward neural networks

NASA Astrophysics Data System (ADS)

Shirvany, Yazdan; Hayati, Mohsen; Moradian, Rostam

2008-12-01

We present a method to solve boundary value problems using artificial neural networks (ANN). A trial solution of the differential equation is written as a feed-forward neural network containing adjustable parameters (the weights and biases). From the differential equation and its boundary conditions we prepare the energy function which is used in the back-propagation method with momentum term to update the network parameters. We improved energy function of ANN which is derived from Schrodinger equation and the boundary conditions. With this improvement of energy function we can use unsupervised training method in the ANN for solving the equation. Unsupervised training aims to minimize a non-negative energy function. We used the ANN method to solve Schrodinger equation for few quantum systems. Eigenfunctions and energy eigenvalues are calculated. Our numerical results are in agreement with their corresponding analytical solution and show the efficiency of ANN method for solving eigenvalue problems.

The Application of Simulation Methods to Intra-Airport Landside Problems.

DOT National Transportation Integrated Search

1975-09-01

This report describes methods of analyzing the flow of people through the airport landside, which is defined as extending between the airport boundary and the arrival/departure gates. Passenger delay for specified flow and holding values is taken as ...

Dynamic history-dependent variational-hemivariational inequalities with applications to contact mechanics

NASA Astrophysics Data System (ADS)

Migórski, Stanislaw; Ogorzaly, Justyna

2017-02-01

In the paper we deliver a new existence and uniqueness result for a class of abstract nonlinear variational-hemivariational inequalities which are governed by two operators depending on the history of the solution, and include two nondifferentiable functionals, a convex and a nonconvex one. Then, we consider an initial boundary value problem which describes a model of evolution of a viscoelastic body in contact with a foundation. The contact process is assumed to be dynamic, and the friction is described by subdifferential boundary conditions. Both the constitutive law and the contact condition involve memory operators. As an application of the abstract theory, we provide a result on the unique weak solvability of the contact problem.

Numerical Recovering of a Speed of Sound by the BC-Method in 3D

NASA Astrophysics Data System (ADS)

Pestov, Leonid; Bolgova, Victoria; Danilin, Alexandr

We develop the numerical algorithm for solving the inverse problem for the wave equation by the Boundary Control method. The problem, which we refer to as a forward one, is an initial boundary value problem for the wave equation with zero initial data in the bounded domain. The inverse problem is to find the speed of sound c(x) by the measurements of waves induced by a set of boundary sources. The time of observation is assumed to be greater then two acoustical radius of the domain. The numerical algorithm for sound reconstruction is based on two steps. The first one is to find a (sufficiently large) number of controls {f_j} (the basic control is defined by the position of the source and some time delay), which generates the same number of known harmonic functions, i.e. Δ {u_j}(.,T) = 0 , where {u_j} is the wave generated by the control {f_j} . After that the linear integral equation w.r.t. the speed of sound is obtained. The piecewise constant model of the speed is used. The result of numerical testing of 3-dimensional model is presented.

High-Order Accurate Solutions to the Helmholtz Equation in the Presence of Boundary Singularities

NASA Astrophysics Data System (ADS)

Britt, Darrell Steven, Jr.

Problems of time-harmonic wave propagation arise in important fields of study such as geological surveying, radar detection/evasion, and aircraft design. These often involve highfrequency waves, which demand high-order methods to mitigate the dispersion error. We propose a high-order method for computing solutions to the variable-coefficient inhomogeneous Helmholtz equation in two dimensions on domains bounded by piecewise smooth curves of arbitrary shape with a finite number of boundary singularities at known locations. We utilize compact finite difference (FD) schemes on regular structured grids to achieve highorder accuracy due to their efficiency and simplicity, as well as the capability to approximate variable-coefficient differential operators. In this work, a 4th-order compact FD scheme for the variable-coefficient Helmholtz equation on a Cartesian grid in 2D is derived and tested. The well known limitation of finite differences is that they lose accuracy when the boundary curve does not coincide with the discretization grid, which is a severe restriction on the geometry of the computational domain. Therefore, the algorithm presented in this work combines high-order FD schemes with the method of difference potentials (DP), which retains the efficiency of FD while allowing for boundary shapes that are not aligned with the grid without sacrificing the accuracy of the FD scheme. Additionally, the theory of DP allows for the universal treatment of the boundary conditions. One of the significant contributions of this work is the development of an implementation that accommodates general boundary conditions (BCs). In particular, Robin BCs with discontinuous coefficients are studied, for which we introduce a piecewise parameterization of the boundary curve. Problems with discontinuities in the boundary data itself are also studied. We observe that the design convergence rate suffers whenever the solution loses regularity due to the boundary conditions. This is because the FD scheme is only consistent for classical solutions of the PDE. For this reason, we implement the method of singularity subtraction as a means for restoring the design accuracy of the scheme in the presence of singularities at the boundary. While this method is well studied for low order methods and for problems in which singularities arise from the geometry (e.g., corners), we adapt it to our high-order scheme for curved boundaries via a conformal mapping and show that it can also be used to restore accuracy when the singularity arises from the BCs rather than the geometry. Altogether, the proposed methodology for 2D boundary value problems is computationally efficient, easily handles a wide class of boundary conditions and boundary shapes that are not aligned with the discretization grid, and requires little modification for solving new problems.

PAN AIR summary document (version 1.0)

NASA Technical Reports Server (NTRS)

Derbyshire, T.; Sidwell, K. W.

1982-01-01

The capabilities and limitations of the panel aerodynamics (PAN AIR) computer program system are summarized. This program uses a higher order panel method to solve boundary value problems involving the Prandtl-Glauert equation for subsonic and supersonic potential flows. Both aerodynamic and hydrodynamic problems can be solved using this modular software which is written for the CDC 6600 and 7600, and the CYBER 170 series computers.

PGA/MOEAD: a preference-guided evolutionary algorithm for multi-objective decision-making problems with interval-valued fuzzy preferences

NASA Astrophysics Data System (ADS)

Luo, Bin; Lin, Lin; Zhong, ShiSheng

2018-02-01

In this research, we propose a preference-guided optimisation algorithm for multi-criteria decision-making (MCDM) problems with interval-valued fuzzy preferences. The interval-valued fuzzy preferences are decomposed into a series of precise and evenly distributed preference-vectors (reference directions) regarding the objectives to be optimised on the basis of uniform design strategy firstly. Then the preference information is further incorporated into the preference-vectors based on the boundary intersection approach, meanwhile, the MCDM problem with interval-valued fuzzy preferences is reformulated into a series of single-objective optimisation sub-problems (each sub-problem corresponds to a decomposed preference-vector). Finally, a preference-guided optimisation algorithm based on MOEA/D (multi-objective evolutionary algorithm based on decomposition) is proposed to solve the sub-problems in a single run. The proposed algorithm incorporates the preference-vectors within the optimisation process for guiding the search procedure towards a more promising subset of the efficient solutions matching the interval-valued fuzzy preferences. In particular, lots of test instances and an engineering application are employed to validate the performance of the proposed algorithm, and the results demonstrate the effectiveness and feasibility of the algorithm.

On Complex Water Conflicts: Role of Enabling Conditions for Pragmatic Resolution

NASA Astrophysics Data System (ADS)

Islam, S.; Choudhury, E.

2016-12-01

Many of our current and emerging water problems are interconnected and cross boundaries, domains, scales, and sectors. These boundary crossing water problems are neither static nor linear; but often are interconnected nonlinearly with other problems and feedback. The solution space for these complex problems - involving interdependent variables, processes, actors, and institutions - can't be pre-stated. We need to recognize the disconnect among values, interests, and tools as well as problems, policies, and politics. Scientific and technological solutions are desired for efficiency and reliability, but need to be politically feasible and actionable. Governing and managing complex water problems require difficult tradeoffs in exploring and sharing benefits and burdens through carefully crafted negotiation processes. The crafting of such negotiation process, we argue, constitutes a pragmatic approach to negotiation - one that is based on the identification of enabling conditions - as opposed to mechanistic casual explanations, and rooted in contextual conditions to specify and ensure the principles of equity and sustainability. We will use two case studies to demonstrate the efficacy of the proposed principled pragmatic approcah to address complex water problems.

Strong Asymmetric Limit of the Quasi-Potential of the Boundary Driven Weakly Asymmetric Exclusion Process

NASA Astrophysics Data System (ADS)

Bertini, Lorenzo; Gabrielli, Davide; Landim, Claudio

2009-07-01

We consider the weakly asymmetric exclusion process on a bounded interval with particles reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers equation with Dirichlet boundary conditions. In the case in which the bulk asymmetry is in the same direction as the drift due to the boundary reservoirs, we prove that the quasi-potential can be expressed in terms of the solution to a one-dimensional boundary value problem which has been introduced by Enaud and Derrida [16]. We consider the strong asymmetric limit of the quasi-potential and recover the functional derived by Derrida, Lebowitz, and Speer [15] for the asymmetric exclusion process.

Exact semi-separation of variables in waveguides with non-planar boundaries

NASA Astrophysics Data System (ADS)

Athanassoulis, G. A.; Papoutsellis, Ch. E.

2017-05-01

Series expansions of unknown fields Φ =∑φn Zn in elongated waveguides are commonly used in acoustics, optics, geophysics, water waves and other applications, in the context of coupled-mode theories (CMTs). The transverse functions Zn are determined by solving local Sturm-Liouville problems (reference waveguides). In most cases, the boundary conditions assigned to Zn cannot be compatible with the physical boundary conditions of Φ, leading to slowly convergent series, and rendering CMTs mild-slope approximations. In the present paper, the heuristic approach introduced in Athanassoulis & Belibassakis (Athanassoulis & Belibassakis 1999 J. Fluid Mech. 389, 275-301) is generalized and justified. It is proved that an appropriately enhanced series expansion becomes an exact, rapidly convergent representation of the field Φ, valid for any smooth, non-planar boundaries and any smooth enough Φ. This series expansion can be differentiated termwise everywhere in the domain, including the boundaries, implementing an exact semi-separation of variables for non-separable domains. The efficiency of the method is illustrated by solving a boundary value problem for the Laplace equation, and computing the corresponding Dirichlet-to-Neumann operator, involved in Hamiltonian equations for nonlinear water waves. The present method provides accurate results with only a few modes for quite general domains. Extensions to general waveguides are also discussed.

Global uniqueness in an inverse problem for time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Kian, Y.; Oksanen, L.; Soccorsi, E.; Yamamoto, M.

2018-01-01

Given (M , g), a compact connected Riemannian manifold of dimension d ⩾ 2, with boundary ∂M, we consider an initial boundary value problem for a fractional diffusion equation on (0 , T) × M, T > 0, with time-fractional Caputo derivative of order α ∈ (0 , 1) ∪ (1 , 2). We prove uniqueness in the inverse problem of determining the smooth manifold (M , g) (up to an isometry), and various time-independent smooth coefficients appearing in this equation, from measurements of the solutions on a subset of ∂M at fixed time. In the "flat" case where M is a compact subset of Rd, two out the three coefficients ρ (density), a (conductivity) and q (potential) appearing in the equation ρ ∂tα u - div (a∇u) + qu = 0 on (0 , T) × M are recovered simultaneously.

Three-dimensional electrical impedance tomography: a topology optimization approach.

PubMed

Mello, Luís Augusto Motta; de Lima, Cícero Ribeiro; Amato, Marcelo Britto Passos; Lima, Raul Gonzalez; Silva, Emílio Carlos Nelli

2008-02-01

Electrical impedance tomography is a technique to estimate the impedance distribution within a domain, based on measurements on its boundary. In other words, given the mathematical model of the domain, its geometry and boundary conditions, a nonlinear inverse problem of estimating the electric impedance distribution can be solved. Several impedance estimation algorithms have been proposed to solve this problem. In this paper, we present a three-dimensional algorithm, based on the topology optimization method, as an alternative. A sequence of linear programming problems, allowing for constraints, is solved utilizing this method. In each iteration, the finite element method provides the electric potential field within the model of the domain. An electrode model is also proposed (thus, increasing the accuracy of the finite element results). The algorithm is tested using numerically simulated data and also experimental data, and absolute resistivity values are obtained. These results, corresponding to phantoms with two different conductive materials, exhibit relatively well-defined boundaries between them, and show that this is a practical and potentially useful technique to be applied to monitor lung aeration, including the possibility of imaging a pneumothorax.

A combined application of boundary-element and Runge-Kutta methods in three-dimensional elasticity and poroelasticity

NASA Astrophysics Data System (ADS)

Igumnov, Leonid; Ipatov, Aleksandr; Belov, Aleksandr; Petrov, Andrey

2015-09-01

The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach boundary integral equations of 3-D isotropic linear theories of elasticity and poroelasticity in Laplace transforms. Poroelastic media are described using Biot models with four and five base functions. With the help of the boundary-element method, solutions in time are obtained, using the stepped method of numerically inverting Laplace transform on the nodes of Runge-Kutta methods. The boundary-element method is used in combination with the collocation method, local element-by-element approximation based on the matched interpolation model. The results of analyzing wave problems of the effect of a non-stationary force on elastic and poroelastic finite bodies, a poroelastic half-space (also with a fictitious boundary) and a layered half-space weakened by a cavity, and a half-space with a trench are presented. Excitation of a slow wave in a poroelastic medium is studied, using the stepped BEM-scheme on the nodes of Runge-Kutta methods.

Regularization of moving boundaries in a laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results.

PubMed

Meulenbroek, Bernard; Ebert, Ute; Schäfer, Lothar

2005-11-04

The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact uniformly propagating solutions of this problem in 2D and construct a single partial differential equation governing small perturbations of these solutions. For some parameter value, this equation can be solved analytically, which shows rigorously that the uniformly propagating solution is linearly convectively stable and that the asymptotic relaxation is universal and exponential in time.

Non-modal analysis of the diocotron instability for cylindrical geometry with conducting boundary

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mikhailenko, V. V.; Seok Kim, Jin; Jo, Younghyun

2014-05-15

The temporal evolution of the linear diocotron instability of a cylindrical annular plasma column surrounded by a conducting boundary has been investigated by using the methodology of the cylindrical shearing modes. The linear solution of the initial and boundary-value problems is obtained which is valid for any time at which linear effects dominate. The solution reveals that the initial perturbations of the electron density pass through the stage of the non-modal evolution when the perturbation experiences spatio-temporal distortion pertinent to the considered geometry of the electron column. The result is confirmed by a two-dimensional cylindrical particle-in-cell simulation.

Stable boundary conditions and difference schemes for Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Dutt, P.

1985-01-01

The Navier-Stokes equations can be viewed as an incompletely elliptic perturbation of the Euler equations. By using the entropy function for the Euler equations as a measure of energy for the Navier-Stokes equations, it was possible to obtain nonlinear energy estimates for the mixed initial boundary value problem. These estimates are used to derive boundary conditions which guarantee L2 boundedness even when the Reynolds number tends to infinity. Finally, a new difference scheme for modelling the Navier-Stokes equations in multidimensions for which it is possible to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation was proposed.

Three-dimensional elastic stress and displacement analysis of finite circular geometry solids containing cracks

NASA Technical Reports Server (NTRS)

Gyekenyesi, J. P.; Mendelson, A.; Kring, J.

1973-01-01

A seminumerical method is presented for solving a set of coupled partial differential equations subject to mixed and coupled boundary conditions. The use of this method is illustrated by obtaining solutions for two circular geometry and mixed boundary value problems in three-dimensional elasticity. Stress and displacement distributions are calculated in an axisymmetric, circular bar of finite dimensions containing a penny-shaped crack. Approximate results for an annular plate containing internal surface cracks are also presented.

A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation.

PubMed

Gumerov, Nail A; Duraiswami, Ramani

2009-01-01

The development of a fast multipole method (FMM) accelerated iterative solution of the boundary element method (BEM) for the Helmholtz equations in three dimensions is described. The FMM for the Helmholtz equation is significantly different for problems with low and high kD (where k is the wavenumber and D the domain size), and for large problems the method must be switched between levels of the hierarchy. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements), and these errors must be balanced against approximations introduced by the FMM and the convergence criterion for iterative solution. These different errors must all be chosen in a way that, on the one hand, excess work is not done and, on the other, that the error achieved by the overall computation is acceptable. Details of translation operators for low and high kD, choice of representations, and BEM quadrature schemes, all consistent with these approximations, are described. A novel preconditioner using a low accuracy FMM accelerated solver as a right preconditioner is also described. Results of the developed solvers for large boundary value problems with 0.0001 less, similarkD less, similar500 are presented and shown to perform close to theoretical expectations.

Diffraction of Electromagnetic Waves on a Waveguide Joint

NASA Astrophysics Data System (ADS)

Malykh, Mikhail; Sevastianov, Leonid; Tyutyunnik, Anastasiya; Nikolaev, Nikolai

2018-02-01

In general, the investigation of the electromagnetic field in an inhomogeneous waveguide doesn't reduce to the study of two independent boundary value problems for the Helmholtz equation. We show how to rewrite the Helmholtz equations in the "Hamiltonian form" to express the connection between these two problems explicitly. The problem of finding monochromatic waves in an arbitrary waveguide is reduced to an infinite system of ordinary differential equations in a properly constructed Hilbert space. The calculations are performed in the computer algebra system Sage.

Accurate Projection Methods for the Incompressible Navier–Stokes Equations

DOE PAGES

Brown, David L.; Cortez, Ricardo; Minion, Michael L.

2001-04-10

This paper considers the accuracy of projection method approximations to the initial–boundary-value problem for the incompressible Navier–Stokes equations. The issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second-order methodology a decade and a half ago. It has been observed that while the velocity can be reliably computed to second-order accuracy in time and space, the pressure is typically only first-order accurate in the L ∞-norm. Here, we identify the source of this problem in the interplay of the global pressure-update formula with the numerical boundary conditions and presentsmore » an improved projection algorithm which is fully second-order accurate, as demonstrated by a normal mode analysis and numerical experiments. In addition, a numerical method based on a gauge variable formulation of the incompressible Navier–Stokes equations, which provides another option for obtaining fully second-order convergence in both velocity and pressure, is discussed. The connection between the boundary conditions for projection methods and the gauge method is explained in detail.« less

An Application of the Difference Potentials Method to Solving External Problems in CFD

NASA Technical Reports Server (NTRS)

Ryaben 'Kii, Victor S.; Tsynkov, Semyon V.

1997-01-01

Numerical solution of infinite-domain boundary-value problems requires some special techniques that would make the problem available for treatment on the computer. Indeed, the problem must be discretized in a way that the computer operates with only finite amount of information. Therefore, the original infinite-domain formulation must be altered and/or augmented so that on one hand the solution is not changed (or changed slightly) and on the other hand the finite discrete formulation becomes available. One widely used approach to constructing such discretizations consists of truncating the unbounded original domain and then setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The role of the ABC's is to close the truncated problem and at the same time to ensure that the solution found inside the finite computational domain would be maximally close to (in the ideal case, exactly the same as) the corresponding fragment of the original infinite-domain solution. Let us emphasize that the proper treatment of artificial boundaries may have a profound impact on the overall quality and performance of numerical algorithms. The latter statement is corroborated by the numerous computational experiments and especially concerns the area of CFD, in which external problems present a wide class of practically important formulations. In this paper, we review some work that has been done over the recent years on constructing highly accurate nonlocal ABC's for calculation of compressible external flows. The approach is based on implementation of the generalized potentials and pseudodifferential boundary projection operators analogous to those proposed first by Calderon. The difference potentials method (DPM) by Ryaben'kii is used for the effective computation of the generalized potentials and projections. The resulting ABC's clearly outperform the existing methods from the standpoints of accuracy and robustness, in many cases noticeably speed up the multigrid convergence, and at the same time are quite comparable to other methods from the standpoints of geometric universality and simplicity of implementation.

Boundary Regularity for the Porous Medium Equation

NASA Astrophysics Data System (ADS)

Björn, Anders; Björn, Jana; Gianazza, Ugo; Siljander, Juhana

2018-05-01

We study the boundary regularity of solutions to the porous medium equation {u_t = Δ u^m} in the degenerate range {m > 1} . In particular, we show that in cylinders the Dirichlet problem with positive continuous boundary data on the parabolic boundary has a solution which attains the boundary values, provided that the spatial domain satisfies the elliptic Wiener criterion. This condition is known to be optimal, and it is a consequence of our main theorem which establishes a barrier characterization of regular boundary points for general—not necessarily cylindrical—domains in {{R}^{n+1}} . One of our fundamental tools is a new strict comparison principle between sub- and superparabolic functions, which makes it essential for us to study both nonstrict and strict Perron solutions to be able to develop a fruitful boundary regularity theory. Several other comparison principles and pasting lemmas are also obtained. In the process we obtain a rather complete picture of the relation between sub/superparabolic functions and weak sub/supersolutions.

A Review of Methods for Moving Boundary Problems

DTIC Science & Technology

2009-07-01

the bound- ary value problem for the eikonal equation: ‖∇u‖ = 1 for x ∈ Ω (29) u = 0 for x ∈ Γ (30) ERDC/CHL TR-09-10 8 where ‖ ‖ is the Euclidean norm...Solutions of the eikonal equation can in turn be characterized as steady state solutions of the initial value prob- lem ut + sgn(u0)(‖∇u‖ − 1) = 0...LS using the eikonal equation and use the NCI equation for the LS dynam- ics. The complete system of equations in weak form is ∫ Ω (‖∇u‖ − 1)wdV = 0

A Conforming Multigrid Method for the Pure Traction Problem of Linear Elasticity: Mixed Formulation

NASA Technical Reports Server (NTRS)

Lee, Chang-Ock

1996-01-01

A multigrid method using conforming P-1 finite element is developed for the two-dimensional pure traction boundary value problem of linear elasticity. The convergence is uniform even as the material becomes nearly incompressible. A heuristic argument for acceleration of the multigrid method is discussed as well. Numerical results with and without this acceleration as well as performance estimates on a parallel computer are included.

Making science high impact to inform decision-making: Using boundary objects for aquatic research

EPA Science Inventory

The St. Louis River represents a complex natural resource management problem. Current ecosystem management decisions must address extensive sediment remediation and habitat restoration goals for the lower river and associated port, as well as recreational users who value differen...

Numerical grid generation techniques. [conference

NASA Technical Reports Server (NTRS)

1980-01-01

The state of the art in topology and flow geometry is presented. Solution techniques for partial differential equations are reviewed and included developments in coordinate transformations, conformal mapping, and invariant imbeddings. Applications of these techniques in fluid mechanics, flow geometry, boundary value problems, and fluidics are presented.

Nonlinear Schrödinger approach to European option pricing

NASA Astrophysics Data System (ADS)

Wróblewski, Marcin

2017-05-01

This paper deals with numerical option pricing methods based on a Schrödinger model rather than the Black-Scholes model. Nonlinear Schrödinger boundary value problems seem to be alternatives to linear models which better reflect the complexity and behavior of real markets. Therefore, based on the nonlinear Schrödinger option pricing model proposed in the literature, in this paper a model augmented by external atomic potentials is proposed and numerically tested. In terms of statistical physics the developed model describes the option in analogy to a pair of two identical quantum particles occupying the same state. The proposed model is used to price European call options on a stock index. the model is calibrated using the Levenberg-Marquardt algorithm based on market data. A Runge-Kutta method is used to solve the discretized boundary value problem numerically. Numerical results are provided and discussed. It seems that our proposal more accurately models phenomena observed in the real market than do linear models.

Alternative Attitude Commanding and Control for Precise Spacecraft Landing

NASA Technical Reports Server (NTRS)

Singh, Gurkirpal

2004-01-01

A report proposes an alternative method of control for precision landing on a remote planet. In the traditional method, the attitude of a spacecraft is required to track a commanded translational acceleration vector, which is generated at each time step by solving a two-point boundary value problem. No requirement of continuity is imposed on the acceleration. The translational acceleration does not necessarily vary smoothly. Tracking of a non-smooth acceleration causes the vehicle attitude to exhibit undesirable transients and poor pointing stability behavior. In the alternative method, the two-point boundary value problem is not solved at each time step. A smooth reference position profile is computed. The profile is recomputed only when the control errors get sufficiently large. The nominal attitude is still required to track the smooth reference acceleration command. A steering logic is proposed that controls the position and velocity errors about the reference profile by perturbing the attitude slightly about the nominal attitude. The overall pointing behavior is therefore smooth, greatly reducing the degree of pointing instability.

A scheme to calculate higher-order homogenization as applied to micro-acoustic boundary value problems

NASA Astrophysics Data System (ADS)

Vagh, Hardik A.; Baghai-Wadji, Alireza

2008-12-01

Current technological challenges in materials science and high-tech device industry require the solution of boundary value problems (BVPs) involving regions of various scales, e.g. multiple thin layers, fibre-reinforced composites, and nano/micro pores. In most cases straightforward application of standard variational techniques to BVPs of practical relevance necessarily leads to unsatisfactorily ill-conditioned analytical and/or numerical results. To remedy the computational challenges associated with sub-sectional heterogeneities various sophisticated homogenization techniques need to be employed. Homogenization refers to the systematic process of smoothing out the sub-structural heterogeneities, leading to the determination of effective constitutive coefficients. Ordinarily, homogenization involves a sophisticated averaging and asymptotic order analysis to obtain solutions. In the majority of the cases only zero-order terms are constructed due to the complexity of the processes involved. In this paper we propose a constructive scheme for obtaining homogenized solutions involving higher order terms, and thus, guaranteeing higher accuracy and greater robustness of the numerical results. We present

What is Wrong with the Boundary Conditions in Column Tracer Tests

NASA Astrophysics Data System (ADS)

Zhan, H.

2007-12-01

Solute transport in a column is probably one of the most fundamental problems investigated in contaminant hydrology and soil physics because it serves as a benchmark for testing transport theories, for measuring dispersivities, etc. Despite its importance, there are still dispute and inconsistency on how to deal with the boundary conditions involved in such problems. The boundary condition could impose great influence upon transport in a column, particularly when the length of the column is relatively short, or the so-called Peclet number is not large. There are three types of boundary conditions to choose for transport in a column. Among these three types of boundary conditions, only the third-type boundary satisfies the mass balance requirement rigorously. The first type boundary, despite its frequent use in previous studies, could lead to serious mass balance problems. The most serious problem is on how to deal with the outlet boundary. Some studies have used a zero concentration gradient at the outlet (the so-called Danckwerts' boundary condition). This is named the model A. Another idea is to treat the finite length column as a part of an infinitely long column and to calculate the concentration at the outlet based on a formula developed for an infinitely long column. This is named the model B. The model A satisfies the mass balance requirement but was found to fit with the experimental data poorly. The model B does not satisfy the mass balance requirement, but usually agree well with the experimental data. So, the dilemma is: which model to choose? At present, most investigators prefer to choose the model B because of its close agreement with the experimental data, despite of its violation of the mass balance requirement. But the question is: why the model A, which satisfies the mass balance requirement, does not fit with the experimental data? It turns out that the advection-dispersion equation (ADE) that uses the Fick's first law to describe the hydrodynamic dispersion has some problems, particularly in the regions near the two boundaries. Taylor (1921) has pointed out that the dispersion coefficient varies linearly with time at the beginning and tends to its asymptotic, Fickian value after a travel time of a few correlation scales. Dagan and Bresler (1985) have further pointed out that the constant dispersivity is attained after the solute body has traveled tens of conductivity integral scales. For transport in a homogeneous column, the integral scale of the conductivity is probably around the pore scale or equivalent to the dispersivity value. Therefore, for a finite column whose length is not much greater than the dispersivity value, the transition zones in which solute transport is non-Fickian could consist of a significant portion of the column length. It is such non-Fickian transport in the column that is responsible for the failure of the model A. But still, why does the model B yield the right solution? There is no answer to this question based on a rigorous quantitative analysis yet. To resolve the dilemma, one must carry out a non-Fickian transport study to deal with the transition zones. It is my hypothesis that if the non-Fickian transport analysis succeeds, one will find that the mass balance requirement is indeed satisfied in the model B. Dagan and Bresler (1985) have pointed to the right direction, but a rigorous analysis has not followed. This is something interesting and worthwhile to investigate. REFERENCES CITED Dagan, G., and Bresler, E., 1985. Comment on ¡°Flux-averaged and volume-averaged concentration in continuum approaches to solute transport¡± by J.C. Parker and M.Th. van Genuchten. Water Resources Research, 21: 1299- 1300. Taylor, G.I., 1921. Diffusion by continuous movements. Proc. London Math Soc. 2: 196-212.

Boundary conditions and transmission reflection of electron spin in a quantum well

NASA Astrophysics Data System (ADS)

Dargys, A.

2012-04-01

Boundary conditions for a spinor at the interface of hetero- and homobarrier in the presence of spin-orbit interaction are briefly reviewed and generalized. Then they are applied to 2D electron in the presence of a discontinuity of physical parameters in a quantum well. It is shown that in general case under oblique electron incidence, the problem can be solved analytically and the Fresnel-type formulae for polarization can be obtained if, in addition, the Gröbner basis algorithm is addressed to solve the problem. It is observed that the transmitted and reflected spin polarization may strongly depend on values of spin-orbit constants on both sides of the homobarrier in the quantum well.

Asymptotic theory of circular polarization memory.

PubMed

Dark, Julia P; Kim, Arnold D

2017-09-01

We establish a quantitative theory of circular polarization memory, which is the unexpected persistence of the incident circular polarization state in a strongly scattering medium. Using an asymptotic analysis of the three-dimensional vector radiative transfer equation (VRTE) in the limit of strong scattering, we find that circular polarization memory must occur in a boundary layer near the portion of the boundary on which polarized light is incident. The boundary layer solution satisfies a one-dimensional conservative scattering VRTE. Through a spectral analysis of this boundary layer problem, we introduce the dominant mode, which is the slowest-decaying mode in the boundary layer. To observe circular polarization memory for a particular set of optical parameters, we find that this dominant mode must pass three tests: (1) this dominant mode is given by the largest, discrete eigenvalue of a reduced problem that corresponds to Fourier mode k=0 in the azimuthal angle, and depends only on Stokes parameters U and V; (2) the polarization state of this dominant mode is largely circular polarized so that |V|≫|U|; and (3) the circular polarization of this dominant mode is maintained for all directions so that V is sign-definite. By applying these three tests to numerical calculations for monodisperse distributions of Mie scatterers, we determine the values of the size and relative refractive index when circular polarization memory occurs. In addition, we identify a reduced, scalar-like problem that provides an accurate approximation for the dominant mode when circular polarization memory occurs.

Estimating surface acoustic impedance with the inverse method.

PubMed

Piechowicz, Janusz

2011-01-01

Sound field parameters are predicted with numerical methods in sound control systems, in acoustic designs of building and in sound field simulations. Those methods define the acoustic properties of surfaces, such as sound absorption coefficients or acoustic impedance, to determine boundary conditions. Several in situ measurement techniques were developed; one of them uses 2 microphones to measure direct and reflected sound over a planar test surface. Another approach is used in the inverse boundary elements method, in which estimating acoustic impedance of a surface is expressed as an inverse boundary problem. The boundary values can be found from multipoint sound pressure measurements in the interior of a room. This method can be applied to arbitrarily-shaped surfaces. This investigation is part of a research programme on using inverse methods in industrial room acoustics.

A new extrapolation cascadic multigrid method for three dimensional elliptic boundary value problems

NASA Astrophysics Data System (ADS)

Pan, Kejia; He, Dongdong; Hu, Hongling; Ren, Zhengyong

2017-09-01

In this paper, we develop a new extrapolation cascadic multigrid method, which makes it possible to solve three dimensional elliptic boundary value problems with over 100 million unknowns on a desktop computer in half a minute. First, by combining Richardson extrapolation and quadratic finite element (FE) interpolation for the numerical solutions on two-level of grids (current and previous grids), we provide a quite good initial guess for the iterative solution on the next finer grid, which is a third-order approximation to the FE solution. And the resulting large linear system from the FE discretization is then solved by the Jacobi-preconditioned conjugate gradient (JCG) method with the obtained initial guess. Additionally, instead of performing a fixed number of iterations as used in existing cascadic multigrid methods, a relative residual tolerance is introduced in the JCG solver, which enables us to obtain conveniently the numerical solution with the desired accuracy. Moreover, a simple method based on the midpoint extrapolation formula is proposed to achieve higher-order accuracy on the finest grid cheaply and directly. Test results from four examples including two smooth problems with both constant and variable coefficients, an H3-regular problem as well as an anisotropic problem are reported to show that the proposed method has much better efficiency compared to the classical V-cycle and W-cycle multigrid methods. Finally, we present the reason why our method is highly efficient for solving these elliptic problems.

Design of supercritical swept wings

NASA Technical Reports Server (NTRS)

Garabedian, P.; Mcfadden, G.

1982-01-01

Computational fluid dynamics are used to discuss problems inherent to transonic three-dimensional flow past supercritical swept wings. The formulation for a boundary value problem for the flow past the wing is provided, including consideration of weak shock waves and the use of parabolic coordinates. A swept wing code is developed which requires a mesh of 152 x 10 x 12 points and 200 time cycles. A formula for wave drag is calculated, based on the idea that the conservation form of the momentum equation becomes an entropy inequality measuring the drag, expressible in terms of a small-disturbance equation for a potential function in two dimensions. The entropy inequality has been incorporated in a two-dimensional code for the analysis of transonic flow over airfoils. A method of artificial viscosity is explored for optimum pressure distributions with design, and involves a free boundary problem considering speed over only a portion of the wing.

Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics

NASA Astrophysics Data System (ADS)

Farrell, Patricio; Koprucki, Thomas; Fuhrmann, Jürgen

2017-10-01

We compare three thermodynamically consistent numerical fluxes known in the literature, appearing in a Voronoï finite volume discretization of the van Roosbroeck system with general charge carrier statistics. Our discussion includes an extension of the Scharfetter-Gummel scheme to non-Boltzmann (e.g. Fermi-Dirac) statistics. It is based on the analytical solution of a two-point boundary value problem obtained by projecting the continuous differential equation onto the interval between neighboring collocation points. Hence, it serves as a reference flux. The exact solution of the boundary value problem can be approximated by computationally cheaper fluxes which modify certain physical quantities. One alternative scheme averages the nonlinear diffusion (caused by the non-Boltzmann nature of the problem), another one modifies the effective density of states. To study the differences between these three schemes, we analyze the Taylor expansions, derive an error estimate, visualize the flux error and show how the schemes perform for a carefully designed p-i-n benchmark simulation. We present strong evidence that the flux discretization based on averaging the nonlinear diffusion has an edge over the scheme based on modifying the effective density of states.

Using complexity science and negotiation theory to resolve boundary-crossing water issues

NASA Astrophysics Data System (ADS)

Islam, Shafiqul; Susskind, Lawrence

2018-07-01

Many water governance and management issues are complex. The complexity of these issues is related to crossing of multiple boundaries: political, social and jurisdictional, as well as physical, ecological and biogeochemical. Resolution of these issues usually requires interactions of many parties with conflicting values and interests operating across multiple boundaries and scales to make decisions. The interdependence and feedback among interacting variables, processes, actors and institutions are hard to model and difficult to forecast. Thus, decision-making related to complex water problems needs be contingent and adaptive. This paper draws on a number of ideas from complexity science and negotiation theory that may make it easier to cope with the complexities and difficulties of managing boundary crossing water disputes. It begins with the Water Diplomacy Framework that was developed and tested over the past several years. Then, it uses three key ideas from complexity science (interdependence and interconnectedness; uncertainty and feedback; emergence and adaptation) and three from negotiation theory (stakeholder identification and engagement; joint fact finding; and value creation through option generation) to show how application of these ideas can help enhance effectiveness of water management.

Global existence and exponential decay of the solution for a viscoelastic wave equation with a delay

NASA Astrophysics Data System (ADS)

Dai, Qiuyi; Yang, Zhifeng

2014-10-01

In this paper, we consider initial-boundary value problem of viscoelastic wave equation with a delay term in the interior feedback. Namely, we study the following equation together with initial-boundary conditions of Dirichlet type in Ω × (0, + ∞) and prove that for arbitrary real numbers μ 1 and μ 2, the above-mentioned problem has a unique global solution under suitable assumptions on the kernel g. This improve the results of the previous literature such as Nicaise and Pignotti (SIAM J. Control Optim 45:1561-1585, 2006) and Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011) by removing the restriction imposed on μ 1 and μ 2. Furthermore, we also get an exponential decay results for the energy of the concerned problem in the case μ 1 = 0 which solves an open problem proposed by Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011).

Two-phase Hele-Shaw flow with a moving contact line

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weinstein, S.J.; Ungar, L.H.; Dussan, E.B.

1988-01-01

An asymptotic analysis is presented for Hele-Shaw viscous fingering with a moving contact line at flow rates. As in problems where a thin film is present instead of a contact line, the narrow gap limit is nonuniform, and interfacial boundary conditions valid for the Hele-Shaw equations must be determined in order to predict the flow field and interface shape. Many well-posed boundary-value problems can be identified, each corresponding to a different flow regime characterized by the relative sizes of the capillary number (dimensionless velocity) and the dimensionless gap width. These problems incorporate terms corresponding to the gapwise component of themore » interfacial curvature (the curvature in the cross-sectional view of the Hele-Shaw cell) and spanwise curvature (seen in the top view of the cell) in different ways. Nonunique interface solutions typically arise as in the analogous thin film problems. The relationships between the curvature terms, the spectra of allowable solutions, and the implications for stability are discussed.« less

Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem

NASA Astrophysics Data System (ADS)

Lakshtanov, E.; Vainberg, B.

2013-10-01

The paper concerns the isotropic interior transmission eigenvalue (ITE) problem. This problem is not elliptic, but we show that, using the Dirichlet-to-Neumann map, it can be reduced to an elliptic one. This leads to the discreteness of the spectrum as well as to certain results on a possible location of the transmission eigenvalues. If the index of refraction \\sqrt{n(x)} is real, then we obtain a result on the existence of infinitely many positive ITEs and the Weyl-type lower bound on its counting function. All the results are obtained under the assumption that n(x) - 1 does not vanish at the boundary of the obstacle or it vanishes identically, but its normal derivative does not vanish at the boundary. We consider the classical transmission problem as well as the case when the inhomogeneous medium contains an obstacle. Some results on the discreteness and localization of the spectrum are obtained for complex valued n(x).

Spheroidal Integral Equations for Geodetic Inversion of Geopotential Gradients

NASA Astrophysics Data System (ADS)

Novák, Pavel; Šprlák, Michal

2018-03-01

The static Earth's gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth's surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet's boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green's kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth.

Modeling of non-ideal hard permanent magnets with an affine-linear model, illustrated for a bar and a horseshoe magnet

NASA Astrophysics Data System (ADS)

Glane, Sebastian; Reich, Felix A.; Müller, Wolfgang H.

2017-11-01

This study is dedicated to continuum-scale material modeling of isotropic permanent magnets. An affine-linear extension to the commonly used ideal hard model for permanent magnets is proposed, motivated, and detailed. In order to demonstrate the differences between these models, bar and horseshoe magnets are considered. The structure of the boundary value problem for the magnetic field and related solution techniques are discussed. For the ideal model, closed-form analytical solutions were obtained for both geometries. Magnetic fields of the boundary value problems for both models and differently shaped magnets were computed numerically by using the boundary element method. The results show that the character of the magnetic field is strongly influenced by the model that is used. Furthermore, it can be observed that the shape of an affine-linear magnet influences the near-field significantly. Qualitative comparisons with experiments suggest that both the ideal and the affine-linear models are relevant in practice, depending on the magnetic material employed. Mathematically speaking, the ideal magnetic model is a special case of the affine-linear one. Therefore, in applications where knowledge of the near-field is important, the affine-linear model can yield more accurate results—depending on the magnetic material.

Multiple positive solutions to nonlinear boundary value problems of a system for fractional differential equations.

PubMed

Zhai, Chengbo; Hao, Mengru

2014-01-01

By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by -D(0+)(ν1)y1(t) = λ1a1(t)f(y1(t), y2(t)), - D(0+)(ν2)y2(t) = λ2a2(t)g(y1(t), y2(t)), where D(0+)(ν) is the standard Riemann-Liouville fractional derivative, ν1, ν2 ∈ (n - 1, n] for n > 3 and n ∈ N, subject to the boundary conditions y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = 0 = [D(0+ (α)y2(t)] t=1, for 1 ≤ α ≤ n - 2, or y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = ϕ1(y1), [D(0+)(α)y2(t)] t=1 = ϕ2(y2), for 1 ≤ α ≤ n - 2, ϕ1, ϕ2 ∈ C([0,1], R). Our results are new and complement previously known results. As an application, we also give an example to demonstrate our result.

Solving Fluid Structure Interaction Problems with an Immersed Boundary Method

NASA Technical Reports Server (NTRS)

Barad, Michael F.; Brehm, Christoph; Kiris, Cetin C.

2016-01-01

An immersed boundary method for the compressible Navier-Stokes equations can be used for moving boundary problems as well as fully coupled fluid-structure interaction is presented. The underlying Cartesian immersed boundary method of the Launch Ascent and Vehicle Aerodynamics (LAVA) framework, based on the locally stabilized immersed boundary method previously presented by the authors, is extended to account for unsteady boundary motion and coupled to linear and geometrically nonlinear structural finite element solvers. The approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems. Keywords: Immersed Boundary Method, Higher-Order Finite Difference Method, Fluid Structure Interaction.

Analysis of the Large Urban Fire Environment. Part II. Parametric Analysis and Model City Simulations.

DTIC Science & Technology

1982-11-01

algorithm for turning-region boundary value problem -70- d. Program control parameters: ALPHA (Qq) max’ maximum value of Qq in present coding. BETA, BLOSS...Parameters available for either system descrip- tion or program control . (These parameters are currently unused, so they are set equal to zero.) IGUESS...Parameter that controls the initial choices of first-shoot values along y = 0. IGUESS = 1: Discretized versions of P(r, 0), T(r, 0), and u(r, 0) must

Numerical Determination of Critical Conditions for Thermal Ignition

NASA Technical Reports Server (NTRS)

Luo, W.; Wake, G. C.; Hawk, C. W.; Litchford, R. J.

2008-01-01

The determination of ignition or thermal explosion in an oxidizing porous body of material, as described by a dimensionless reaction-diffusion equation of the form .tu = .2u + .e-1/u over the bounded region O, is critically reexamined from a modern perspective using numerical methodologies. First, the classic stationary model is revisited to establish the proper reference frame for the steady-state solution space, and it is demonstrated how the resulting nonlinear two-point boundary value problem can be reexpressed as an initial value problem for a system of first-order differential equations, which may be readily solved using standard algorithms. Then, the numerical procedure is implemented and thoroughly validated against previous computational results based on sophisticated path-following techniques. Next, the transient nonstationary model is attacked, and the full nonlinear form of the reaction-diffusion equation, including a generalized convective boundary condition, is discretized and expressed as a system of linear algebraic equations. The numerical methodology is implemented as a computer algorithm, and validation computations are carried out as a prelude to a broad-ranging evaluation of the assembly problem and identification of the watershed critical initial temperature conditions for thermal ignition. This numerical methodology is then used as the basis for studying the relationship between the shape of the critical initial temperature distribution and the corresponding spatial moments of its energy content integral and an attempt to forge a fundamental conjecture governing this relation. Finally, the effects of dynamic boundary conditions on the classic storage problem are investigated and the groundwork is laid for the development of an approximate solution methodology based on adaptation of the standard stationary model.

Documentation of computer program VS2D to solve the equations of fluid flow in variably saturated porous media

USGS Publications Warehouse

Lappala, E.G.; Healy, R.W.; Weeks, E.P.

1987-01-01

This report documents FORTRAN computer code for solving problems involving variably saturated single-phase flow in porous media. The flow equation is written with total hydraulic potential as the dependent variable, which allows straightforward treatment of both saturated and unsaturated conditions. The spatial derivatives in the flow equation are approximated by central differences, and time derivatives are approximated either by a fully implicit backward or by a centered-difference scheme. Nonlinear conductance and storage terms may be linearized using either an explicit method or an implicit Newton-Raphson method. Relative hydraulic conductivity is evaluated at cell boundaries by using either full upstream weighting, the arithmetic mean, or the geometric mean of values from adjacent cells. Nonlinear boundary conditions treated by the code include infiltration, evaporation, and seepage faces. Extraction by plant roots that is caused by atmospheric demand is included as a nonlinear sink term. These nonlinear boundary and sink terms are linearized implicitly. The code has been verified for several one-dimensional linear problems for which analytical solutions exist and against two nonlinear problems that have been simulated with other numerical models. A complete listing of data-entry requirements and data entry and results for three example problems are provided. (USGS)

Finite element modeling of diffusion and partitioning in biological systems: the infinite composite medium problem.

PubMed

Missel, P J

2000-01-01

Four methods are proposed for modeling diffusion in heterogeneous media where diffusion and partition coefficients take on differing values in each subregion. The exercise was conducted to validate finite element modeling (FEM) procedures in anticipation of modeling drug diffusion with regional partitioning into ocular tissue, though the approach can be useful for other organs, or for modeling diffusion in laminate devices. Partitioning creates a discontinuous value in the dependent variable (concentration) at an intertissue boundary that is not easily handled by available general-purpose FEM codes, which allow for only one value at each node. The discontinuity is handled using a transformation on the dependent variable based upon the region-specific partition coefficient. Methods were evaluated by their ability to reproduce a known exact result, for the problem of the infinite composite medium (Crank, J. The Mathematics of Diffusion, 2nd ed. New York: Oxford University Press, 1975, pp. 38-39.). The most physically intuitive method is based upon the concept of chemical potential, which is continuous across an interphase boundary (method III). This method makes the equation of the dependent variable highly nonlinear. This can be linearized easily by a change of variables (method IV). Results are also given for a one-dimensional problem simulating bolus injection into the vitreous, predicting time disposition of drug in vitreous and retina.

Asymptotic stability of a nonlinear Korteweg-de Vries equation with critical lengths

NASA Astrophysics Data System (ADS)

Chu, Jixun; Coron, Jean-Michel; Shang, Peipei

2015-10-01

We study an initial-boundary-value problem of a nonlinear Korteweg-de Vries equation posed on the finite interval (0, 2 kπ) where k is a positive integer. The whole system has Dirichlet boundary condition at the left end-point, and both of Dirichlet and Neumann homogeneous boundary conditions at the right end-point. It is known that the origin is not asymptotically stable for the linearized system around the origin. We prove that the origin is (locally) asymptotically stable for the nonlinear system if the integer k is such that the kernel of the linear Korteweg-de Vries stationary equation is of dimension 1. This is for example the case if k = 1.

On the solution of the generalized wave and generalized sine-Gordon equations

NASA Technical Reports Server (NTRS)

Ablowitz, M. J.; Beals, R.; Tenenblat, K.

1986-01-01

The generalized wave equation and generalized sine-Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two-dimensional versions. In this paper, a system of linear differential equations is associated with these equations, and it is shown how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial-boundary value problem is solved for these equations.

Recent Advances in the Edge-Function Method 1979-1980

DTIC Science & Technology

1980-07-30

the residuals are within the limits within which an engineer can specify the boundary conditions of the problem, then the corresponding Mathematical ...truncation lvel . The consistent preference shown by the solver routine for verteA functions as opposed to polar functions reinforces the expectations of...Accordingly,each solution zr_.-4_des a Mathematical Model for the given physical problem- R.M.S. values provide a practical criterion for the enai--er to

Dynamical theory of stability for elastic rods with nonlinear curvature and twist

NASA Technical Reports Server (NTRS)

Wauer, J.

1977-01-01

Considering non-linear terms in the curvature as well as in the twist, the governing boundary value problem for lateral bending of elastic, transverse loaded rods is formulated by means of Hamilton's principle. Using the method of small vibrations, the associated linearized equations of stability are derived, which complete the currently accepted relations. The example of the simplest lateral bending problem illustrates the improved effect of the proposed equations.

Traveling-wave solutions in continuous chains of unidirectionally coupled oscillators

NASA Astrophysics Data System (ADS)

Glyzin, S. D.; Kolesov, A. Yu; Rozov, N. Kh

2017-12-01

Proposed is a mathematical model of a continuous annular chain of unidirectionally coupled generators given by certain nonlinear advection-type hyperbolic boundary value problem. Such problems are constructed by a limit transition from annular chains of unidirectionally coupled ordinary differential equations with an unbounded increase in the number of links. It is shown that any preassigned finite number of stable periodic motions of the traveling-wave type can coexist in the model.

Postbuckling and vibration of end-supported elastica pipes conveying fluid and columns under follower loads

NASA Astrophysics Data System (ADS)

Plaut, R. H.

2006-01-01

Fluid-conveying pipes with supported ends buckle when the fluid velocity reaches a critical value. For higher velocities, the postbuckled equilibrium shape can be directly related to that for a column under a follower end load. However, the corresponding vibration frequencies are different due to the Coriolis force associated with the fluid flow. Clamped-clamped, pinned-pinned, and clamped-pinned pipes are considered first. Axial sliding is permitted at the downstream end. The pipe is modeled as an inextensible elastica. The equilibrium shape may have large displacements, and small motions about that shape are analyzed. The behavior is conservative in the prebuckling range and nonconservative in the postbuckling range (during which the Coriolis force does work and the motions decay). Next, related columns are studied, first with a concentrated follower load at the axially sliding end, and then with a distributed follower load. In all cases, a shooting method is used to solve the nonlinear boundary-value problem for the equilibrium configuration, and to solve the linear boundary-value problem for the first four vibration frequencies. The results for the three different types of loading are compared.

On the role of acoustic feedback in boundary-layer instability.

PubMed

Wu, Xuesong

2014-07-28

In this paper, the classical triple-deck formalism is employed to investigate two instability problems in which an acoustic feedback loop plays an essential role. The first concerns a subsonic boundary layer over a flat plate on which two well-separated roughness elements are present. A spatially amplifying Tollmien-Schlichting (T-S) wave between the roughness elements is scattered by the downstream roughness to emit a sound wave that propagates upstream and impinges on the upstream roughness to regenerate the T-S wave, thereby forming a closed feedback loop in the streamwise direction. Numerical calculations suggest that, at high Reynolds numbers and for moderate roughness heights, the long-range acoustic coupling may lead to absolute instability, which is characterized by self-sustained oscillations at discrete frequencies. The dominant peak frequency may jump from one value to another as the Reynolds number, or the distance between the roughness elements, is varied gradually. The second problem concerns the supersonic 'twin boundary layers' that develop along two well-separated parallel flat plates. The two boundary layers are in mutual interaction through the impinging and reflected acoustic waves. It is found that the interaction leads to a new instability that is absent in the unconfined boundary layer. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Direct Numerical Simulation of Automobile Cavity Tones

NASA Technical Reports Server (NTRS)

Kurbatskii, Konstantin; Tam, Christopher K. W.

2000-01-01

The Navier Stokes equation is solved computationally by the Dispersion-Relation-Preserving (DRP) scheme for the flow and acoustic fields associated with a laminar boundary layer flow over an automobile door cavity. In this work, the flow Reynolds number is restricted to R(sub delta*) < 3400; the range of Reynolds number for which laminar flow may be maintained. This investigation focuses on two aspects of the problem, namely, the effect of boundary layer thickness on the cavity tone frequency and intensity and the effect of the size of the computation domain on the accuracy of the numerical simulation. It is found that the tone frequency decreases with an increase in boundary layer thickness. When the boundary layer is thicker than a certain critical value, depending on the flow speed, no tone is emitted by the cavity. Computationally, solutions of aeroacoustics problems are known to be sensitive to the size of the computation domain. Numerical experiments indicate that the use of a small domain could result in normal mode type acoustic oscillations in the entire computation domain leading to an increase in tone frequency and intensity. When the computation domain is expanded so that the boundaries are at least one wavelength away from the noise source, the computed tone frequency and intensity are found to be computation domain size independent.

Characteristic Evolution and Matching

NASA Astrophysics Data System (ADS)

Winicour, Jeffrey

2012-01-01

I review the development of numerical evolution codes for general relativity based upon the characteristic initial-value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D-axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black-hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black-hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.

Hybrid near-optimal aeroassisted orbit transfer plane change trajectories

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Duckeman, Gregory A.

1994-01-01

In this paper, a hybrid methodology is used to determine optimal open loop controls for the atmospheric portion of the aeroassisted plane change problem. The method is hybrid in the sense that it combines the features of numerical collocation with the analytically tractable portions of the problem which result when the two-point boundary value problem is cast in the form of a regular perturbation problem. Various levels of approximation are introduced by eliminating particular collocation parameters and their effect upon problem complexity and required number of nodes is discussed. The results include plane changes of 10, 20, and 30 degrees for a given vehicle.

Control optimization of a lifting body entry problem by an improved and a modified method of perturbation function. Ph.D. Thesis - Houston Univ.

NASA Technical Reports Server (NTRS)

Garcia, F., Jr.

1974-01-01

A study of the solution problem of a complex entry optimization was studied. The problem was transformed into a two-point boundary value problem by using classical calculus of variation methods. Two perturbation methods were devised. These methods attempted to desensitize the contingency of the solution of this type of problem on the required initial co-state estimates. Also numerical results are presented for the optimal solution resulting from a number of different initial co-states estimates. The perturbation methods were compared. It is found that they are an improvement over existing methods.

Nonlinear Resonance and Duffing's Spring Equation

ERIC Educational Resources Information Center

Fay, Temple H.

2006-01-01

This note discusses the boundary in the frequency--amplitude plane for boundedness of solutions to the forced spring Duffing type equation. For fixed initial conditions and fixed parameter [epsilon] results are reported of a systematic numerical investigation on the global stability of solutions to the initial value problem as the parameters F and…

A First Step towards Variational Methods in Engineering

ERIC Educational Resources Information Center

Periago, Francisco

2003-01-01

In this paper, a didactical proposal is presented to introduce the variational methods for solving boundary value problems to engineering students. Starting from a couple of simple models arising in linear elasticity and heat diffusion, the concept of weak solution for these models is motivated and the existence, uniqueness and continuous…

Computation of Nonlinear Backscattering Using a High-Order Numerical Method

NASA Technical Reports Server (NTRS)

Fibich, G.; Ilan, B.; Tsynkov, S.

2001-01-01

The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.

A superlinear convergence estimate for an iterative method for the biharmonic equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horn, M.A.

In [CDH] a method for the solution of boundary value problems for the biharmonic equation using conformal mapping was investigated. The method is an implementation of the classical method of Muskhelishvili. In [CDH] it was shown, using the Hankel structure, that the linear system in [Musk] is the discretization of the identify plus a compact operator, and therefore the conjugate gradient method will converge superlinearly. The purpose of this paper is to give an estimate of the superlinear convergence in the case when the boundary curve is in a Hoelder class.

A non-asymptotic homogenization theory for periodic electromagnetic structures.

PubMed

Tsukerman, Igor; Markel, Vadim A

2014-08-08

Homogenization of electromagnetic periodic composites is treated as a two-scale problem and solved by approximating the fields on both scales with eigenmodes that satisfy Maxwell's equations and boundary conditions as accurately as possible. Built into this homogenization methodology is an error indicator whose value characterizes the accuracy of homogenization. The proposed theory allows one to define not only bulk, but also position-dependent material parameters (e.g. in proximity to a physical boundary) and to quantify the trade-off between the accuracy of homogenization and its range of applicability to various illumination conditions.

Thermo-viscoelastic analysis of composite materials

NASA Technical Reports Server (NTRS)

Lin, Kuen Y.; Hwang, I. H.

1989-01-01

The thermo-viscoelastic boundary value problem for anisotropic materials is formulated and a numerical procedure is developed for the efficient analysis of stress and deformation histories in composites. The procedure is based on the finite element method and therefore it is applicable to composite laminates containing geometric discontinuities and complicated boundary conditions. Using the present formulation, the time-dependent stress and strain distributions in both notched and unnotched graphite/epoxy composites have been obtained. The effect of temperature and ply orientation on the creep and relaxation response is also studied.

TOPICAL REVIEW: The stability for the Cauchy problem for elliptic equations

NASA Astrophysics Data System (ADS)

Alessandrini, Giovanni; Rondi, Luca; Rosset, Edi; Vessella, Sergio

2009-12-01

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality. Due to the current absence of research funding from the Italian Ministry of University and Research, this work has been completed without any financial support.

Modular Approaches to Earth Science Scientific Computing: 3D Electromagnetic Induction Modeling as an Example

NASA Astrophysics Data System (ADS)

Tandon, K.; Egbert, G.; Siripunvaraporn, W.

2003-12-01

We are developing a modular system for three-dimensional inversion of electromagnetic (EM) induction data, using an object oriented programming approach. This approach allows us to modify the individual components of the inversion scheme proposed, and also reuse the components for variety of problems in earth science computing howsoever diverse they might be. In particular, the modularity allows us to (a) change modeling codes independently of inversion algorithm details; (b) experiment with new inversion algorithms; and (c) modify the way prior information is imposed in the inversion to test competing hypothesis and techniques required to solve an earth science problem. Our initial code development is for EM induction equations on a staggered grid, using iterative solution techniques in 3D. An example illustrated here is an experiment with the sensitivity of 3D magnetotelluric inversion to uncertainties in the boundary conditions required for regional induction problems. These boundary conditions should reflect the large-scale geoelectric structure of the study area, which is usually poorly constrained. In general for inversion of MT data, one fixes boundary conditions at the edge of the model domain, and adjusts the earth?s conductivity structure within the modeling domain. Allowing for errors in specification of the open boundary values is simple in principle, but no existing inversion codes that we are aware of have this feature. Adding a feature such as this is straightforward within the context of the modular approach. More generally, a modular approach provides an efficient methodology for setting up earth science computing problems to test various ideas. As a concrete illustration relevant to EM induction problems, we investigate the sensitivity of MT data near San Andreas Fault at Parkfield (California) to uncertainties in the regional geoelectric structure.

Directive sources in acoustic discrete-time domain simulations based on directivity diagrams.

PubMed

Escolano, José; López, José J; Pueo, Basilio

2007-06-01

Discrete-time domain methods provide a simple and flexible way to solve initial boundary value problems. With regard to the sources in such methods, only monopoles or dipoles can be considered. However, in many problems such as room acoustics, the radiation of realistic sources is directional-dependent and their directivity patterns have a clear influence on the total sound field. In this letter, a method to synthesize the directivity of sources is proposed, especially in cases where the knowledge is only based on discrete values of the directivity diagram. Some examples have been carried out in order to show the behavior and accuracy of the proposed method.

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries.

PubMed

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

A Curved, Elastostatic Boundary Element for Plane Anisotropic Structures

NASA Technical Reports Server (NTRS)

Smeltzer, Stanley S.; Klang, Eric C.

2001-01-01

The plane-stress equations of linear elasticity are used in conjunction with those of the boundary element method to develop a novel curved, quadratic boundary element applicable to structures composed of anisotropic materials in a state of plane stress or plane strain. The curved boundary element is developed to solve two-dimensional, elastostatic problems of arbitrary shape, connectivity, and material type. As a result of the anisotropy, complex variables are employed in the fundamental solution derivations for a concentrated unit-magnitude force in an infinite elastic anisotropic medium. Once known, the fundamental solutions are evaluated numerically by using the known displacement and traction boundary values in an integral formulation with Gaussian quadrature. All the integral equations of the boundary element method are evaluated using one of two methods: either regular Gaussian quadrature or a combination of regular and logarithmic Gaussian quadrature. The regular Gaussian quadrature is used to evaluate most of the integrals along the boundary, and the combined scheme is employed for integrals that are singular. Individual element contributions are assembled into the global matrices of the standard boundary element method, manipulated to form a system of linear equations, and the resulting system is solved. The interior displacements and stresses are found through a separate set of auxiliary equations that are derived using an Airy-type stress function in terms of complex variables. The capabilities and accuracy of this method are demonstrated for a laminated-composite plate with a central, elliptical cutout that is subjected to uniform tension along one of the straight edges of the plate. Comparison of the boundary element results for this problem with corresponding results from an analytical model show a difference of less than 1%.

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries

NASA Astrophysics Data System (ADS)

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

Evolution of solar magnetic fields - A new approach to MHD initial-boundary value problems by the method of nearcharacteristics

NASA Technical Reports Server (NTRS)

Nakagawa, Y.

1980-01-01

A method of analysis for the MHD initial-boundary problem is presented in which the model's formulation is based on the method of nearcharacteristics developed by Werner (1968) and modified by Shin and Kot (1978). With this method, the physical causality relationship can be traced from the perturbation to the response as in the method of characteristics, while achieving the advantage of a considerable reduction in mathematical procedures. The method offers the advantage of examining not only the evolution of nonforce free fields, but also the changes of physical conditions in the atmosphere accompanying the evolution of magnetic fields. The physical validity of the method is demonstrated with examples, and their significance in interpreting observations is discussed.

Boundaries for algebras of holomorphic functions on Marcinkiewicz sequence spaces

NASA Astrophysics Data System (ADS)

Choi, Yun Sung; Han, Kwang Hee

2006-11-01

Let be the Banach algebra of all complex-valued bounded continuous functions on the closed unit ball BE of a complex Banach space E and holomorphic in the interior of BE and let be the closed subalgebra of those functions which are uniformly continuous on BE. For the case whose bidual is a Marcinkiewicz sequence space Mw, we describe some sufficient conditions for a set to be a boundary of either or . Moreover, we consider some analogous problems on to those which were studied on the Gowers space Gp of characteristic p by Grados and Moraes [L.R. Grados, L.A. Moraes, Boundaries for algebras of holomorphic functions, J. Math. Anal. Appl. 281 (2003) 575-586; L.R. Grados, L.A. Moraes, Boundaries for an algebra of bounded holomorphic functions, J. Korean Math. Soc. 41 (1) (2004) 231-242].

Step scaling and the Yang-Mills gradient flow

NASA Astrophysics Data System (ADS)

Lüscher, Martin

2014-06-01

The use of the Yang-Mills gradient flow in step-scaling studies of lattice QCD is expected to lead to results of unprecedented precision. Step scaling is usually based on the Schrödinger functional, where time ranges over an interval [0 , T] and all fields satisfy Dirichlet boundary conditions at time 0 and T. In these calculations, potentially important sources of systematic errors are boundary lattice effects and the infamous topology-freezing problem. The latter is here shown to be absent if Neumann instead of Dirichlet boundary conditions are imposed on the gauge field at time 0. Moreover, the expectation values of gauge-invariant local fields at positive flow time (and of other well localized observables) that reside in the center of the space-time volume are found to be largely insensitive to the boundary lattice effects.

The Application of a Boundary Integral Equation Method to the Prediction of Ducted Fan Engine Noise

NASA Technical Reports Server (NTRS)

Dunn, M. H.; Tweed, J.; Farassat, F.

1999-01-01

The prediction of ducted fan engine noise using a boundary integral equation method (BIEM) is considered. Governing equations for the BIEM are based on linearized acoustics and describe the scattering of incident sound by a thin, finite-length cylindrical duct in the presence of a uniform axial inflow. A classical boundary value problem (BVP) is derived that includes an axisymmetric, locally reacting liner on the duct interior. Using potential theory, the BVP is recast as a system of hypersingular boundary integral equations with subsidiary conditions. We describe the integral equation derivation and solution procedure in detail. The development of the computationally efficient ducted fan noise prediction program TBIEM3D, which implements the BIEM, and its utility in conducting parametric noise reduction studies are discussed. Unlike prediction methods based on spinning mode eigenfunction expansions, the BIEM does not require the decomposition of the interior acoustic field into its radial and axial components which, for the liner case, avoids the solution of a difficult complex eigenvalue problem. Numerical spectral studies are presented to illustrate the nexus between the eigenfunction expansion representation and BIEM results. We demonstrate BIEM liner capability by examining radiation patterns for several cases of practical interest.

Asymptotic theory of two-dimensional trailing-edge flows

NASA Technical Reports Server (NTRS)

Melnik, R. E.; Chow, R.

1975-01-01

Problems of laminar and turbulent viscous interaction near trailing edges of streamlined bodies are considered. Asymptotic expansions of the Navier-Stokes equations in the limit of large Reynolds numbers are used to describe the local solution near the trailing edge of cusped or nearly cusped airfoils at small angles of attack in compressible flow. A complicated inverse iterative procedure, involving finite-difference solutions of the triple-deck equations coupled with asymptotic solutions of the boundary values, is used to accurately solve the viscous interaction problem. Results are given for the correction to the boundary-layer solution for drag of a finite flat plate at zero angle of attack and for the viscous correction to the lift of an airfoil at incidence. A rational asymptotic theory is developed for treating turbulent interactions near trailing edges and is shown to lead to a multilayer structure of turbulent boundary layers. The flow over most of the boundary layer is described by a Lighthill model of inviscid rotational flow. The main features of the model are discussed and a sample solution for the skin friction is obtained and compared with the data of Schubauer and Klebanoff for a turbulent flow in a moderately large adverse pressure gradient.

The general solution to the classical problem of finite Euler Bernoulli beam

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Amba-Rao, C. L.

1977-01-01

An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.

Numerical simulation of transient, incongruent vaporization induced by high power laser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsai, C.H.

1981-01-01

A mathematical model and numerical calculations were developed to solve the heat and mass transfer problems specifically for uranum oxide subject to laser irradiation. It can easily be modified for other heat sources or/and other materials. In the uranium-oxygen system, oxygen is the preferentially vaporizing component, and as a result of the finite mobility of oxygen in the solid, an oxygen deficiency is set up near the surface. Because of the bivariant behavior of uranium oxide, the heat transfer problem and the oxygen diffusion problem are coupled and a numerical method of simultaneously solving the two boundary value problems ismore » studied. The temperature dependence of the thermal properties and oxygen diffusivity, as well as the highly ablative effect on the surface, leads to considerable non-linearities in both the governing differential equations and the boundary conditions. Based on the earlier work done in this laboratory by Olstad and Olander on Iron and on Zirconium hydride, the generality of the problem is expanded and the efficiency of the numerical scheme is improved. The finite difference method, along with some advanced numerical techniques, is found to be an efficient way to solve this problem.« less

A finite element formulation for supersonic flows around complex configurations

NASA Technical Reports Server (NTRS)

Morino, L.

1974-01-01

The problem of small perturbation potential supersonic flow around complex configurations is considered. This problem requires the solution of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the small perturbation boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element are assumed to be constant and equal to its value at the centroid of the element. This yields a set of linear algebraic equations whose coefficients are given by source and doublet integrals over the surface elements. Closed form evaluations of the integrals are presented.

Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography

NASA Astrophysics Data System (ADS)

Medl'a, Matej; Mikula, Karol; Čunderlík, Róbert; Macák, Marek

2018-01-01

The paper presents a numerical solution of the oblique derivative boundary value problem on and above the Earth's topography using the finite volume method (FVM). It introduces a novel method for constructing non-uniform hexahedron 3D grids above the Earth's surface. It is based on an evolution of a surface, which approximates the Earth's topography, by mean curvature. To obtain optimal shapes of non-uniform 3D grid, the proposed evolution is accompanied by a tangential redistribution of grid nodes. Afterwards, the Laplace equation is discretized using FVM developed for such a non-uniform grid. The oblique derivative boundary condition is treated as a stationary advection equation, and we derive a new upwind type discretization suitable for non-uniform 3D grids. The discretization of the Laplace equation together with the discretization of the oblique derivative boundary condition leads to a linear system of equations. The solution of this system gives the disturbing potential in the whole computational domain including the Earth's surface. Numerical experiments aim to show properties and demonstrate efficiency of the developed FVM approach. The first experiments study an experimental order of convergence of the method. Then, a reconstruction of the harmonic function on the Earth's topography, which is generated from the EGM2008 or EIGEN-6C4 global geopotential model, is presented. The obtained FVM solutions show that refining of the computational grid leads to more precise results. The last experiment deals with local gravity field modelling in Slovakia using terrestrial gravity data. The GNSS-levelling test shows accuracy of the obtained local quasigeoid model.

Numerical Boundary Conditions for Computational Aeroacoustics Benchmark Problems

NASA Technical Reports Server (NTRS)

Tam, Chritsopher K. W.; Kurbatskii, Konstantin A.; Fang, Jun

1997-01-01

Category 1, Problems 1 and 2, Category 2, Problem 2, and Category 3, Problem 2 are solved computationally using the Dispersion-Relation-Preserving (DRP) scheme. All these problems are governed by the linearized Euler equations. The resolution requirements of the DRP scheme for maintaining low numerical dispersion and dissipation as well as accurate wave speeds in solving the linearized Euler equations are now well understood. As long as 8 or more mesh points per wavelength is employed in the numerical computation, high quality results are assured. For the first three categories of benchmark problems, therefore, the real challenge is to develop high quality numerical boundary conditions. For Category 1, Problems 1 and 2, it is the curved wall boundary conditions. For Category 2, Problem 2, it is the internal radiation boundary conditions inside the duct. For Category 3, Problem 2, they are the inflow and outflow boundary conditions upstream and downstream of the blade row. These are the foci of the present investigation. Special nonhomogeneous radiation boundary conditions that generate the incoming disturbances and at the same time allow the outgoing reflected or scattered acoustic disturbances to leave the computation domain without significant reflection are developed. Numerical results based on these boundary conditions are provided.

The Effect of Map Boundary on Estimates of Landscape Resistance to Animal Movement

PubMed Central

Koen, Erin L.; Garroway, Colin J.; Wilson, Paul J.; Bowman, Jeff

2010-01-01

Background Artificial boundaries on a map occur when the map extent does not cover the entire area of study; edges on the map do not exist on the ground. These artificial boundaries might bias the results of animal dispersal models by creating artificial barriers to movement for model organisms where there are no barriers for real organisms. Here, we characterize the effects of artificial boundaries on calculations of landscape resistance to movement using circuit theory. We then propose and test a solution to artificially inflated resistance values whereby we place a buffer around the artificial boundary as a substitute for the true, but unknown, habitat. Methodology/Principal Findings We randomly assigned landscape resistance values to map cells in the buffer in proportion to their occurrence in the known map area. We used circuit theory to estimate landscape resistance to organism movement and gene flow, and compared the output across several scenarios: a habitat-quality map with artificial boundaries and no buffer, a map with a buffer composed of randomized habitat quality data, and a map with a buffer composed of the true habitat quality data. We tested the sensitivity of the randomized buffer to the possibility that the composition of the real but unknown buffer is biased toward high or low quality. We found that artificial boundaries result in an overestimate of landscape resistance. Conclusions/Significance Artificial map boundaries overestimate resistance values. We recommend the use of a buffer composed of randomized habitat data as a solution to this problem. We found that resistance estimated using the randomized buffer did not differ from estimates using the real data, even when the composition of the real data was varied. Our results may be relevant to those interested in employing Circuitscape software in landscape connectivity and landscape genetics studies. PMID:20668690

Stability analysis of spectral methods for hyperbolic initial-boundary value systems

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Lustman, L.; Tadmor, E.

1986-01-01

A constant coefficient hyperbolic system in one space variable, with zero initial data is discussed. Dissipative boundary conditions are imposed at the two points x = + or - 1. This problem is discretized by a spectral approximation in space. Sufficient conditions under which the spectral numerical solution is stable are demonstrated - moreover, these conditions have to be checked only for scalar equations. The stability theorems take the form of explicit bounds for the norm of the solution in terms of the boundary data. The dependence of these bounds on N, the number of points in the domain (or equivalently the degree of the polynomials involved), is investigated for a class of standard spectral methods, including Chebyshev and Legendre collocations.

Boundary control for a constrained two-link rigid-flexible manipulator with prescribed performance

NASA Astrophysics Data System (ADS)

Cao, Fangfei; Liu, Jinkun

2018-05-01

In this paper, we consider a boundary control problem for a constrained two-link rigid-flexible manipulator. The nonlinear system is described by hybrid ordinary differential equation-partial differential equation (ODE-PDE) dynamic model. Based on the coupled ODE-PDE model, boundary control is proposed to regulate the joint positions and eliminate the elastic vibration simultaneously. With the help of prescribed performance functions, the tracking error can converge to an arbitrarily small residual set and the convergence rate is no less than a certain pre-specified value. Asymptotic stability of the closed-loop system is rigorously proved by the LaSalle's Invariance Principle extended to infinite-dimensional system. Numerical simulations are provided to demonstrate the effectiveness of the proposed controller.

Two-and three-dimensional unsteady lift problems in high-speed flight

NASA Technical Reports Server (NTRS)

Lomax, Harvard; Heaslet, Max A; Fuller, Franklyn B; Sluder, Loma

1952-01-01

The problem of transient lift on two- and three-dimensional wings flying at high speeds is discussed as a boundary-value problem for the classical wave equation. Kirchoff's formula is applied so that the analysis is reduced, just as in the steady state, to an investigation of sources and doublets. The applications include the evaluation of indicial lift and pitching-moment curves for two-dimensional sinking and pitching wings flying at Mach numbers equal to 0, 0.8, 1.0, 1.2 and 2.0. Results for the sinking case are also given for a Mach number of 0.5. In addition, the indicial functions for supersonic-edged triangular wings in both forward and reverse flow are presented and compared with the two-dimensional values.

On pseudo-spectral time discretizations in summation-by-parts form

NASA Astrophysics Data System (ADS)

Ruggiu, Andrea A.; Nordström, Jan

2018-05-01

Fully-implicit discrete formulations in summation-by-parts form for initial-boundary value problems must be invertible in order to provide well functioning procedures. We prove that, under mild assumptions, pseudo-spectral collocation methods for the time derivative lead to invertible discrete systems when energy-stable spatial discretizations are used.

Building a Sustainable World: Technology, Values, and Social Choices. Peace Education Miniprints No. 41.

ERIC Educational Resources Information Center

Wessels, Michael G.

Planetary life support systems are at risk, and clean air, unpolluted water, and arable land are increasingly scarce. Environmental problems such as ozone depletion and the threat of global warming transcend national boundaries and confront our species with fundamental questions about survival, quality of life, and responsibility to future…

Value Orientations of Candidate Teachers in Knowledge Society

ERIC Educational Resources Information Center

Erdem Keklik, Devrim

2016-01-01

Problem Statement: Enormous changes over the last decades have led to evolving roles of schools, teachers and education itself. This new era of a knowledge society has broadened boundaries of schools, education and learning. Thus, the variables involved in education demand exploration. One of the essential components of education is the teacher.…

Oregon Driver Education. Alcohol/Drugs and Driving.

ERIC Educational Resources Information Center

Oregon State Dept. of Education, Salem. Div. of Curriculum and School Improvement.

This curriculum unit contains 10 modules, to be used in 10 driver education class sessions, on driving under the influence of alcohol and/or other drugs (DUI). The unit aims to combat the Oregon DUI problem, especially among 15- to 24-year-olds, with values clarification, awareness of risk factors and personal boundaries, refusal skills, social…

Determination of the Rotational Barrier in Ethane by Vibrational Spectroscopy and Statistical Thermodynamics

ERIC Educational Resources Information Center

Ercolani, Gianfranco

2005-01-01

The finite-difference boundary-value method is a numerical method suited for the solution of the one-dimensional Schrodinger equation encountered in problems of hindered rotation. Further, the application of the method, in combination with experimental results for the evaluation of the rotational energy barrier in ethane is presented.

On the Hodge-type decomposition and cohomology groups of k-Cauchy-Fueter complexes over domains in the quaternionic space

NASA Astrophysics Data System (ADS)

Chang, Der-Chen; Markina, Irina; Wang, Wei

2016-09-01

The k-Cauchy-Fueter operator D0(k) on one dimensional quaternionic space H is the Euclidean version of spin k / 2 massless field operator on the Minkowski space in physics. The k-Cauchy-Fueter equation for k ≥ 2 is overdetermined and its compatibility condition is given by the k-Cauchy-Fueter complex. In quaternionic analysis, these complexes play the role of Dolbeault complex in several complex variables. We prove that a natural boundary value problem associated to this complex is regular. Then by using the theory of regular boundary value problems, we show the Hodge-type orthogonal decomposition, and the fact that the non-homogeneous k-Cauchy-Fueter equation D0(k) u = f on a smooth domain Ω in H is solvable if and only if f satisfies the compatibility condition and is orthogonal to the set ℋ(k)1 (Ω) of Hodge-type elements. This set is isomorphic to the first cohomology group of the k-Cauchy-Fueter complex over Ω, which is finite dimensional, while the second cohomology group is always trivial.

The CFL condition for spectral approximations to hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Gottlieb, David; Tadmor, Eitan

1991-01-01

The stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients are studied. Time is discretized by explicit multi-level or Runge-Kutta methods of order less than or equal to 3 (forward Euler time differencing is included), and spatial discretizations are studied by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. It is proved that these fully explicit spectral approximations are stable provided their time-step, delta t, is restricted by the CFL-like condition, delta t less than Const. N(exp-2), where N equals the spatial number of degrees of freedom. We give two independent proofs of this result, depending on two different choices of approximate L(exp 2)-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the nonperiodic case.

The CFL condition for spectral approximations to hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Gottlieb, David; Tadmor, Eitan

1990-01-01

The stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients are studied. Time is discretized by explicit multi-level or Runge-Kutta methods of order less than or equal to 3 (forward Euler time differencing is included), and spatial discretizations are studied by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. It is proved that these fully explicit spectral approximations are stable provided their time-step, delta t, is restricted by the CFL-like condition, delta t less than Const. N(exp-2), where N equals the spatial number of degrees of freedom. We give two independent proofs of this result, depending on two different choices of approximate L(exp 2)-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the nonperiodic case.

An extended laser flash technique for thermal diffusivity measurement of high-temperature materials

NASA Technical Reports Server (NTRS)

Shen, F.; Khodadadi, J. M.

1993-01-01

Knowledge of thermal diffusivity data for high-temperature materials (solids and liquids) is very important in analyzing a number of processes, among them solidification, crystal growth, and welding. However, reliable thermal diffusivity versus temperature data, particularly those for high-temperature liquids, are still far from complete. The main measurement difficulties are due to the presence of convection and the requirement for a container. Fortunately, the availability of levitation techniques has made it possible to solve the containment problem. Based on the feasibility of the levitation technology, a new laser flash technique which is applicable to both levitated liquid and solid samples is being developed. At this point, the analysis for solid samples is near completion and highlights of the technique are presented here. The levitated solid sample which is assumed to be a sphere is subjected to a very short burst of high power radiant energy. The temperature of the irradiated surface area is elevated and a transient heat transfer process takes place within the sample. This containerless process is a two-dimensional unsteady heat conduction problem. Due to the nonlinearity of the radiative plus convective boundary condition, an analytic solution cannot be obtained. Two options are available at this point. Firstly, the radiation boundary condition can be linearized, which then accommodates a closed-form analytic solution. Comparison of the analytic curves for the temperature rise at different points to the experimentally-measured values will then provide the thermal diffusivity values. Secondly, one may set up an inverse conduction problem whereby experimentally obtained surface temperature history is used as the boundary conditions. The thermal diffusivity can then be elevated by minimizing the difference between the real heat flux boundary condition (radiation plus convection) and the measurements. Status of an experimental study directed at measuring the thermal diffusivity of high-temperature solid samples of pure Nickel and Inconel 718 superalloys are presented. Preliminary measurements showing surface temperature histories are discussed.

Detection and measurement of tubulitis in renal allograft rejection

NASA Astrophysics Data System (ADS)

Hiller, John B.; Chen, Qi; Jin, Jesse S.; Wang, Yung; Yong, James L. C.

1997-04-01

Tubulitis is one of the most reliable signs of acute renal allograft rejection. It occurs when mononuclear cells are localized between the lining tubular epithelial cells with or without disruption of the tubular basement membrane. It has been found that tubulitis takes place predominantly in the regions of the distal convoluted tubules and the cortical collecting system. The image processing tasks are to find the tubule boundaries and to find the relative location of the lymphocytes and epithelial cells and tubule boundaries. The requirement for accuracy applies to determining the relative locations of the lymphocytes and the tubule boundaries. This paper will show how the different sizes and grey values of the lymphocytes and epithelial cells simplify their identification and location. Difficulties in finding the tubule boundaries image processing will be illustrated. It will be shown how proximate location of epithelial cells and the tubule boundary leads to distortion in determination of the calculated boundary. However, in tubulitis the lymphocytes and the tubule boundaries are proximate.In these cases the tubule boundary is adequately resolved and the image processing is satisfactory to determining relativity in location. An adaptive non-linear anisotropic diffusion process is presented for image filtering and segmentation. Multi-layer analysis is used to extract lymphocytes and tubulitis from images. This paper will discuss grading of tissue using the Banff system. The ability to use computer to use computer processing will be argued as obviating problems of reproducability of values for this classification. This paper will also feature discussion of alternative approaches to image processing and provide an assessment of their capability for improving the identification of the tubule boundaries.

Characteristics of melting heat transfer during flow of Carreau fluid induced by a stretching cylinder.

PubMed

Hashim; Khan, Masood; Saleh Alshomrani, Ali

2017-01-01

This article provides a comprehensive analysis of the energy transportation by virtue of the melting process of high-temperature phase change materials. We have developed a two-dimensional model for the boundary layer flow of non-Newtonian Carreau fluid. It is assumed that flow is caused by stretching of a cylinder in the axial direction by means of a linear velocity. Adequate local similarity transformations are employed to determine a set of non-linear ordinary differential equations which govern the flow problem. Numerical solutions to the resultant non-dimensional boundary value problem are computed via the fifth-order Runge-Kutta Fehlberg integration scheme. The solutions are captured for both zero and non-zero curvature parameters, i.e., for flow over a flat plate or flow over a cylinder. The flow and heat transfer attributes are witnessed to be prompted in an intricate manner by the melting parameter, the curvature parameter, the Weissenberg number, the power law index and the Prandtl number. We determined that one of the possible ways to boost the fluid velocity is to increase the melting parameter. Additionally, both the velocity of the fluid and the momentum boundary layer thickness are higher in the case of flow over a stretching cylinder. As expected, the magnitude of the skin friction and the rate of heat transfer decrease by raising the values of the melting parameter and the Weissenberg number.

Nonlinear hierarchical multiscale modeling of cortical bone considering its nanoscale microstructure.

PubMed

Ghanbari, J; Naghdabadi, R

2009-07-22

We have used a hierarchical multiscale modeling scheme for the analysis of cortical bone considering it as a nanocomposite. This scheme consists of definition of two boundary value problems, one for macroscale, and another for microscale. The coupling between these scales is done by using the homogenization technique. At every material point in which the constitutive model is needed, a microscale boundary value problem is defined using a macroscopic kinematical quantity and solved. Using the described scheme, we have studied elastic properties of cortical bone considering its nanoscale microstructural constituents with various mineral volume fractions. Since the microstructure of bone consists of mineral platelet with nanometer size embedded in a protein matrix, it is similar to the microstructure of soft matrix nanocomposites reinforced with hard nanostructures. Considering a representative volume element (RVE) of the microstructure of bone as the microscale problem in our hierarchical multiscale modeling scheme, the global behavior of bone is obtained under various macroscopic loading conditions. This scheme may be suitable for modeling arbitrary bone geometries subjected to a variety of loading conditions. Using the presented method, mechanical properties of cortical bone including elastic moduli and Poisson's ratios in two major directions and shear modulus is obtained for different mineral volume fractions.

Analytical Solution for Interface Flow to a Sink With an Upconed Saline Water Lens: Strack's Regimes Revisited

NASA Astrophysics Data System (ADS)

Kacimov, A. R.; Obnosov, Y. V.

2018-01-01

A study is made of a steady, two-dimensional groundwater flow with a horizontal well (drain), which pumps out freshwater from an aquifer sandwiched between a horizontal bedrock and ponded soil surface, and containing a lens-shaped static volume of a heavier saline water (DNAPL-dense nonaqueous phase liquid) as a free surface. For flow toward a line sink, an explicit analytical solution is obtained by a conformal mapping of the hexagon in the complex potential plane onto a reference plane and the Keldysh-Sedov integral representation of a mixed boundary-value problem for a complex physical coordinate. The interface is found as a function of the pumping rate, the well locus, the ratio of liquid densities, and the hydraulic heads at the soil surface and in the well. The shape with two inflexion points and fronts varies from a small-thickness bedrock-spread pancake to a critical curvilinear triangle, which cusps toward the sink. The problem is mathematically solvable in a relatively narrow band of geometric and hydraulic parameters. A similar analytic solution for a static heavy bubble confined by a closed-curve interface (no contact with the bedrock) is outlined as an illustration of the method to solve a mixed boundary-value problem.

Application of a low order panel method to complex three-dimensional internal flow problems

NASA Technical Reports Server (NTRS)

Ashby, D. L.; Sandlin, D. R.

1986-01-01

An evaluation of the ability of a low order panel method to predict complex three-dimensional internal flow fields was made. The computer code VSAERO was used as a basis for the evaluation. Guidelines for modeling internal flow geometries were determined and the effects of varying the boundary conditions and the use of numerical approximations on the solutions accuracy were studied. Several test cases were run and the results were compared with theoretical or experimental results. Modeling an internal flow geometry as a closed box with normal velocities specified on an inlet and exit face provided accurate results and gave the user control over the boundary conditions. The values of the boundary conditions greatly influenced the amount of leakage an internal flow geometry suffered and could be adjusted to eliminate leakage. The use of the far-field approximation to reduce computation time influenced the accuracy of a solution and was coupled with the values of the boundary conditions needed to eliminate leakage. The error induced in the influence coefficients by using the far-field approximation was found to be dependent on the type of influence coefficient, the far-field radius, and the aspect ratio of the panels.

Galerkin Spectral Method for the 2D Solitary Waves of Boussinesq Paradigm Equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christou, M. A.; Christov, C. I.

2009-10-29

We consider the 2D stationary propagating solitary waves of the so-called Boussinesq Paradigm equation. The fourth- order elliptic boundary value problem on infinite interval is solved by a Galerkin spectral method. An iterative procedure based on artificial time ('false transients') and operator splitting is used. Results are obtained for the shapes of the solitary waves for different values of the dispersion parameters for both subcritical and supercritical phase speeds.

Matched Interface and Boundary Method for Elasticity Interface Problems

PubMed Central

Wang, Bao; Xia, Kelin; Wei, Guo-Wei

2015-01-01

Elasticity theory is an important component of continuum mechanics and has had widely spread applications in science and engineering. Material interfaces are ubiquity in nature and man-made devices, and often give rise to discontinuous coefficients in the governing elasticity equations. In this work, the matched interface and boundary (MIB) method is developed to address elasticity interface problems. Linear elasticity theory for both isotropic homogeneous and inhomogeneous media is employed. In our approach, Lamé’s parameters can have jumps across the interface and are allowed to be position dependent in modeling isotropic inhomogeneous material. Both strong discontinuity, i.e., discontinuous solution, and weak discontinuity, namely, discontinuous derivatives of the solution, are considered in the present study. In the proposed method, fictitious values are utilized so that the standard central finite different schemes can be employed regardless of the interface. Interface jump conditions are enforced on the interface, which in turn, accurately determines fictitious values. We design new MIB schemes to account for complex interface geometries. In particular, the cross derivatives in the elasticity equations are difficult to handle for complex interface geometries. We propose secondary fictitious values and construct geometry based interpolation schemes to overcome this difficulty. Numerous analytical examples are used to validate the accuracy, convergence and robustness of the present MIB method for elasticity interface problems with both small and large curvatures, strong and weak discontinuities, and constant and variable coefficients. Numerical tests indicate second order accuracy in both L∞ and L2 norms. PMID:25914439

Application of the perfectly matched layer in 2.5D marine controlled-source electromagnetic modeling

NASA Astrophysics Data System (ADS)

Li, Gang; Han, Bo

2017-09-01

For the traditional framework of EM modeling algorithms, the Dirichlet boundary is usually used which assumes the field values are zero at the boundaries. This crude condition requires that the boundaries should be sufficiently far away from the area of interest. Although cell sizes could become larger toward the boundaries as electromagnetic wave is propagated diffusively, a large modeling area may still be necessary to mitigate the boundary artifacts. In this paper, the complex frequency-shifted perfectly matched layer (CFS-PML) in stretching Cartesian coordinates is successfully applied to 2.5D frequency-domain marine controlled-source electromagnetic (CSEM) field modeling. By using this PML boundary, one can restrict the modeling area of interest to the target region. Only a few absorbing layers surrounding the computational area can effectively depress the artificial boundary effect without losing the numerical accuracy. A 2.5D marine CSEM modeling scheme with the CFS-PML is developed by using the staggered finite-difference discretization. This modeling algorithm using the CFS-PML is of high accuracy, and shows advantages in computational time and memory saving than that using the Dirichlet boundary. For 3D problem, this computation time and memory saving should be more significant.

Advancing MODFLOW Applying the Derived Vector Space Method

NASA Astrophysics Data System (ADS)

Herrera, G. S.; Herrera, I.; Lemus-García, M.; Hernandez-Garcia, G. D.

2015-12-01

The most effective domain decomposition methods (DDM) are non-overlapping DDMs. Recently a new approach, the DVS-framework, based on an innovative discretization method that uses a non-overlapping system of nodes (the derived-nodes), was introduced and developed by I. Herrera et al. [1, 2]. Using the DVS-approach a group of four algorithms, referred to as the 'DVS-algorithms', which fulfill the DDM-paradigm (i.e. the solution of global problems is obtained by resolution of local problems exclusively) has been derived. Such procedures are applicable to any boundary-value problem, or system of such equations, for which a standard discretization method is available and then software with a high degree of parallelization can be constructed. In a parallel talk, in this AGU Fall Meeting, Ismael Herrera will introduce the general DVS methodology. The application of the DVS-algorithms has been demonstrated in the solution of several boundary values problems of interest in Geophysics. Numerical examples for a single-equation, for the cases of symmetric, non-symmetric and indefinite problems were demonstrated before [1,2]. For these problems DVS-algorithms exhibited significantly improved numerical performance with respect to standard versions of DDM algorithms. In view of these results our research group is in the process of applying the DVS method to a widely used simulator for the first time, here we present the advances of the application of this method for the parallelization of MODFLOW. Efficiency results for a group of tests will be presented. References [1] I. Herrera, L.M. de la Cruz and A. Rosas-Medina. Non overlapping discretization methods for partial differential equations, Numer Meth Part D E, (2013). [2] Herrera, I., & Contreras Iván "An Innovative Tool for Effectively Applying Highly Parallelized Software To Problems of Elasticity". Geofísica Internacional, 2015 (In press)

Robust multiscale field-only formulation of electromagnetic scattering

NASA Astrophysics Data System (ADS)

Sun, Qiang; Klaseboer, Evert; Chan, Derek Y. C.

2017-01-01

We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric E and magnetic H fields and with the scalar functions (r .E ) and (r .H ) where r is a position vector, the problem can be cast as having to solve a set of scalar Helmholtz equations for the field components that are coupled by the usual electromagnetic boundary conditions at material boundaries. This facilitates a direct solution for the surface values of E and H rather than having to work with surface currents or surface charge densities as intermediate quantities in existing methods. Consequently, our formulation is free of the well-known numerical instability that occurs in the zero-frequency or long-wavelength limit in traditional surface integral solutions of Maxwell's equations and our numerical results converge uniformly to the static results in the long-wavelength limit. Furthermore, we use a formulation of the scalar Helmholtz equation that is expressed as classically convergent integrals and does not require the evaluation of principal value integrals or any knowledge of the solid angle. Therefore, standard quadrature and higher order surface elements can readily be used to improve numerical precision for the same number of degrees of freedom. In addition, near and far field values can be calculated with equal precision, and multiscale problems in which the scatterers possess characteristic length scales that are both large and small relative to the wavelength can be easily accommodated. From this we obtain results for the scattering and transmission of electromagnetic waves at dielectric boundaries that are valid for any ratio of the local surface curvature to the wave number. This is a generalization of the familiar Fresnel formula and Snell's law, valid at planar dielectric boundaries, for the scattering and transmission of electromagnetic waves at surfaces of arbitrary curvature. Implementation details are illustrated with scattering by multiple perfect electric conductors as well as dielectric bodies with complex geometries and composition.

3DGRAPE - THREE DIMENSIONAL GRIDS ABOUT ANYTHING BY POISSON'S EQUATION

NASA Technical Reports Server (NTRS)

Sorenson, R. L.

1994-01-01

The ability to treat arbitrary boundary shapes is one of the most desirable characteristics of a method for generating grids. 3DGRAPE is designed to make computational grids in or about almost any shape. These grids are generated by the solution of Poisson's differential equations in three dimensions. The program automatically finds its own values for inhomogeneous terms which give near-orthogonality and controlled grid cell height at boundaries. Grids generated by 3DGRAPE have been applied to both viscous and inviscid aerodynamic problems, and to problems in other fluid-dynamic areas. 3DGRAPE uses zones to solve the problem of warping one cube into the physical domain in real-world computational fluid dynamics problems. In a zonal approach, a physical domain is divided into regions, each of which maps into its own computational cube. It is believed that even the most complicated physical region can be divided into zones, and since it is possible to warp a cube into each zone, a grid generator which is oriented to zones and allows communication across zonal boundaries (where appropriate) solves the problem of topological complexity. 3DGRAPE expects to read in already-distributed x,y,z coordinates on the bodies of interest, coordinates which will remain fixed during the entire grid-generation process. The 3DGRAPE code makes no attempt to fit given body shapes and redistribute points thereon. Body-fitting is a formidable problem in itself. The user must either be working with some simple analytical body shape, upon which a simple analytical distribution can be easily effected, or must have available some sophisticated stand-alone body-fitting software. 3DGRAPE does not require the user to supply the block-to-block boundaries nor the shapes of the distribution of points. 3DGRAPE will typically supply those block-to-block boundaries simply as surfaces in the elliptic grid. Thus at block-to-block boundaries the following conditions are obtained: (1) grids lines will match up as they approach the block-to-block boundary from either side, (2) grid lines will cross the boundary with no slope discontinuity, (3) the spacing of points along the line piercing the boundary will be continuous, (4) the shape of the boundary will be consistent with the surrounding grid, and (5) the distribution of points on the boundary will be reasonable in view of the surrounding grid. 3DGRAPE offers a powerful building-block approach to complex 3-D grid generation, but is a low-level tool. Users may build each face of each block as they wish, from a wide variety of resources. 3DGRAPE uses point-successive-over-relaxation (point-SOR) to solve the Poisson equations. This method is slow, although it does vectorize nicely. Any number of sophisticated graphics programs may be used on the stored output file of 3DGRAPE though it lacks interactive graphics. Versatility was a prominent consideration in developing the code. The block structure allows a great latitude in the problems it can treat. As the acronym implies, this program should be able to handle just about any physical region into which a computational cube or cubes can be warped. 3DGRAPE was written in FORTRAN 77 and should be machine independent. It was originally developed on a Cray under COS and tested on a MicroVAX 3200 under VMS 5.1.

Atmospheric effect in three-space scenario for the Stokes-Helmert method of geoid determination

NASA Astrophysics Data System (ADS)

Yang, H.; Tenzer, R.; Vanicek, P.; Santos, M.

2004-05-01

: According to the Stokes-Helmert method for the geoid determination by Vanicek and Martinec (1994) and Vanicek et al. (1999), the Helmert gravity anomalies are computed at the earth surface. To formulate the fundamental formula of physical geodesy, Helmert's gravity anomalies are then downward continued from the earth surface onto the geoid. This procedure, i.e., the inverse Dirichlet's boundary value problem, is realized by solving the Poisson integral equation. The above mentioned "classical" approach can be modified so that the inverse Dirichlet's boundary value problem is solved in the No Topography (NT) space (Vanicek et al., 2004) instead of in the Helmert (H) space. This technique has been introduced by Vanicek et al. (2003) and was used by Tenzer and Vanicek (2003) for the determination of the geoid in the region of the Canadian Rocky Mountains. According to this new approach, the gravity anomalies referred to the earth surface are first transformed into the NT-space. This transformation is realized by subtracting the gravitational attraction of topographical and atmospheric masses from the gravity anomalies at the earth surface. Since the NT-anomalies are harmonic above the geoid, the Dirichlet boundary value problem is solved in the NT-space instead of the Helmert space according to the standard formulation. After being obtained on the geoid, the NT-anomalies are transformed into the H-space to minimize the indirect effect on the geoidal heights. This step, i.e., transformation from NT-space to H-space is realized by adding the gravitational attraction of condensed topographical and condensed atmospheric masses to the NT-anomalies at the geoid. The effects of atmosphere in the standard Stokes-Helmert method was intensively investigated by Sjöberg (1998 and 1999), and Novák (2000). In this presentation, the effect of the atmosphere in the three-space scenario for the Stokes-Helmert method is discussed and the numerical results over Canada are shown. Key words: Atmosphere - Geoid - Gravity

Developments in boundary element methods - 2

NASA Astrophysics Data System (ADS)

Banerjee, P. K.; Shaw, R. P.

This book is a continuation of the effort to demonstrate the power and versatility of boundary element methods which began in Volume 1 of this series. While Volume 1 was designed to introduce the reader to a selected range of problems in engineering for which the method has been shown to be efficient, the present volume has been restricted to time-dependent problems in engineering. Boundary element formulation for melting and solidification problems in considered along with transient flow through porous elastic media, applications of boundary element methods to problems of water waves, and problems of general viscous flow. Attention is given to time-dependent inelastic deformation of metals by boundary element methods, the determination of eigenvalues by boundary element methods, transient stress analysis of tunnels and caverns of arbitrary shape due to traveling waves, an analysis of hydrodynamic loads by boundary element methods, and acoustic emissions from submerged structures.

Feedback Implementation of Zermelo's Optimal Control by Sugeno Approximation

NASA Technical Reports Server (NTRS)

Clifton, C.; Homaifax, A.; Bikdash, M.

1997-01-01

This paper proposes an approach to implement optimal control laws of nonlinear systems in real time. Our methodology does not require solving two-point boundary value problems online and may not require it off-line either. The optimal control law is learned using the original Sugeno controller (OSC) from a family of optimal trajectories. We compare the trajectories generated by the OSC and the trajectories yielded by the optimal feedback control law when applied to Zermelo's ship steering problem.

Mathematical Modeling of Resonant Processes in Confined Geometry of Atomic and Atom-Ion Traps

NASA Astrophysics Data System (ADS)

Melezhik, Vladimir S.

2018-02-01

We discuss computational aspects of the developed mathematical models for resonant processes in confined geometry of atomic and atom-ion traps. The main attention is paid to formulation in the nondirect product discrete-variable representation (npDVR) of the multichannel scattering problem with nonseparable angular part in confining traps as the boundary-value problem. Computational efficiency of this approach is demonstrated in application to atomic and atom-ion confinement-induced resonances we predicted recently.

Exact Green's function method of solar force-free magnetic-field computations with constant alpha. I - Theory and basic test cases

NASA Technical Reports Server (NTRS)

Chiu, Y. T.; Hilton, H. H.

1977-01-01

Exact closed-form solutions to the solar force-free magnetic-field boundary-value problem are obtained for constant alpha in Cartesian geometry by a Green's function approach. The uniqueness of the physical problem is discussed. Application of the exact results to practical solar magnetic-field calculations is free of series truncation errors and is at least as economical as the approximate methods currently in use. Results of some test cases are presented.

Vortex instabilities in 3D boundary layers: The relationship between Goertler and crossflow vortices

NASA Technical Reports Server (NTRS)

Bassom, Andrew; Hall, Philip

1990-01-01

The inviscid and viscous stability problems are addressed for a boundary layer which can support both Goertler and crossflow vortices. The change in structure of Goertler vortices is found when the parameter representing the degree of three-dimensionality of the basic boundary layer flow under consideration is increased. It is shown that crossflow vortices emerge naturally as this parameter is increased and ultimately become the only possible vortex instability of the flow. It is shown conclusively that at sufficiently large values of the crossflow there are no unstable Goertler vortices present in a boundary layer which, in the zero crossflow case, is centrifugally unstable. The results suggest that in many practical applications Goertler vortices cannot be a cause of transition because they are destroyed by the 3-D nature of the basic state. In swept wing flows the Goertler mechanism is probably not present for typical angles of sweep of about 20 degrees. Some discussion of the receptivity problem for vortex instabilities in weakly 3-D boundary layers is given; it is shown that inviscid modes have a coupling coefficient marginally smaller than those of the fastest growing viscous modes discussed recently by Denier, Hall, and Seddougui (1990). However the fact that the growth rates of the inviscid modes are the largest in most situations means that they are probably the most likely source of transition.

Hierarchical matrices implemented into the boundary integral approaches for gravity field modelling

NASA Astrophysics Data System (ADS)

Čunderlík, Róbert; Vipiana, Francesca

2017-04-01

Boundary integral approaches applied for gravity field modelling have been recently developed to solve the geodetic boundary value problems numerically, or to process satellite observations, e.g. from the GOCE satellite mission. In order to obtain numerical solutions of "cm-level" accuracy, such approaches require very refined level of the disretization or resolution. This leads to enormous memory requirements that need to be reduced. An implementation of the Hierarchical Matrices (H-matrices) can significantly reduce a numerical complexity of these approaches. A main idea of the H-matrices is based on an approximation of the entire system matrix that is split into a family of submatrices. Large submatrices are stored in factorized representation, while small submatrices are stored in standard representation. This allows reducing memory requirements significantly while improving the efficiency. The poster presents our preliminary results of implementations of the H-matrices into the existing boundary integral approaches based on the boundary element method or the method of fundamental solution.

Topics in spectral methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1985-01-01

After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

NASA Technical Reports Server (NTRS)

Sidi, A.; Israeli, M.

1986-01-01

High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

A non-asymptotic homogenization theory for periodic electromagnetic structures

PubMed Central

Tsukerman, Igor; Markel, Vadim A.

2014-01-01

Homogenization of electromagnetic periodic composites is treated as a two-scale problem and solved by approximating the fields on both scales with eigenmodes that satisfy Maxwell's equations and boundary conditions as accurately as possible. Built into this homogenization methodology is an error indicator whose value characterizes the accuracy of homogenization. The proposed theory allows one to define not only bulk, but also position-dependent material parameters (e.g. in proximity to a physical boundary) and to quantify the trade-off between the accuracy of homogenization and its range of applicability to various illumination conditions. PMID:25104912

Globally Convergent Inverse Reconstruction Algorithm for Detection of IEDs via Imaging of Spatially Distributed Dielectric Constants using Microwave

DTIC Science & Technology

2010-04-27

Dirichlet boundary data DP̃ (x, y) at the entire plane P̃ . Then one can solve the following boundary value problem in the half space below P̃ ∆w − s2w...which we wanted to be a plane wave when reaching the bottom side of the prism of Figure 1, where measurements were conducted. But actually this 14 was a...initializing wave field is a plane wave. On the other hand, a visual inspection of the output experimental data has revealed to us that actually we had a

The mechanical problems on additive manufacturing of viscoelastic solids with integral conditions on a surface increasing in the growth process

NASA Astrophysics Data System (ADS)

Parshin, D. A.; Manzhirov, A. V.

2018-04-01

Quasistatic mechanical problems on additive manufacturing aging viscoelastic solids are investigated. The processes of piecewise-continuous accretion of such solids are considered. The consideration is carried out in the framework of linear mechanics of growing solids. A theorem about commutativity of the integration over an arbitrary surface increasing in the solid growing process and the time-derived integral operator of viscoelasticity with a limit depending on the solid point is proved. This theorem provides an efficient way to construct on the basis of Saint-Venant principle solutions of nonclassical boundary-value problems for describing the mechanical behaviour of additively formed solids with integral satisfaction of boundary conditions on the surfaces expanding due to the additional material influx to the formed solid. The constructed solutions will retrace the evolution of the stress-strain state of the solids under consideration during and after the processes of their additive formation. An example of applying the proved theorem is given.

Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains

NASA Astrophysics Data System (ADS)

Grebenkov, Denis S.; Metzler, Ralf; Oshanin, Gleb

2017-10-01

We study the mean first passage time (MFPT) to a reaction event on a specific site in a cylindrical geometry—characteristic, for instance, for bacterial cells, with a concentric inner cylinder representing the nuclear region of the bacterial cell. A similar problem emerges in the description of a diffusive search by a transcription factor protein for a specific binding region on a single strand of DNA. We develop a unified theoretical approach to study the underlying boundary value problem which is based on a self-consistent approximation of the mixed boundary condition. Our approach permits us to derive explicit, novel, closed-form expressions for the MFPT valid for a generic setting with an arbitrary relation between the system parameters. We analyse this general result in the asymptotic limits appropriate for the above-mentioned biophysical problems. Our investigation reveals the crucial role of the target aspect ratio and of the intrinsic reactivity of the binding region, which were disregarded in previous studies. Theoretical predictions are confirmed by numerical simulations.

The unidirectional motion of two heat-conducting liquids in a flat channel

NASA Astrophysics Data System (ADS)

Andreev, V. K.; Cheremnykh, E. N.

2017-10-01

The unidirectional motion of two viscous incompressible liquids in a flat channel is studied. Liquids contact on a flat interface. External boundaries are fixed solid walls, on which the non-stationary temperature gradients are given. The motion is induced by a joint action of thermogravitational and thermocapillary forces and given total non - stationary fluid flow rate in layers. The corresponding initial boundary value problem is conjugate and inverse because the pressure gradients along axes channel have to be determined together with the velocity and temperature field. For this problem the exact stationary solution is found and a priori estimates of non - stationary solutions are obtained. In Laplace images the solution of the non - stationary problem is found in quadratures. It is proved, that the solution converges to a steady regime with time, if the temperature on the walls and the fluid flow rate are stabilized. The numerical calculations for specific liquid media good agree with the theoretical results.

Advances in Numerical Boundary Conditions for Computational Aeroacoustics

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.

1997-01-01

Advances in Computational Aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high quality numerical boundary treatments. This paper focuses on the recent developments of numerical boundary conditions. In a typical CAA problem, one often encounters two types of boundaries. Because a finite computation domain is used, there are external boundaries. On the external boundaries, boundary conditions simulating the solution outside the computation domain are to be imposed. Inside the computation domain, there may be internal boundaries. On these internal boundaries, boundary conditions simulating the presence of an object or surface with specific acoustic characteristics are to be applied. Numerical boundary conditions, both external or internal, developed for simple model problems are reviewed and examined. Numerical boundary conditions for real aeroacoustic problems are also discussed through specific examples. The paper concludes with a description of some much needed research in numerical boundary conditions for CAA.

Chemorheology of reactive systems: Finite element analysis

NASA Technical Reports Server (NTRS)

Douglas, C.; Roylance, D.

1982-01-01

The equations which govern the nonisothermal flow of reactive fluids are outlined, and the means by which finite element analysis is used to solve these equations for the sort of arbitrary boundary conditions encountered in industrial practice are described. The performance of the computer code is illustrated by several trial problems, selected more for their value in providing insight to polymer processing flows than as practical production problems. Although a good deal remains to be learned as to the performance and proper use of this numerical technique, it is undeniably useful in providing better understanding of today's complicated polymer processing problems.

Domain decomposition for a mixed finite element method in three dimensions

USGS Publications Warehouse

Cai, Z.; Parashkevov, R.R.; Russell, T.F.; Wilson, J.D.; Ye, X.

2003-01-01

We consider the solution of the discrete linear system resulting from a mixed finite element discretization applied to a second-order elliptic boundary value problem in three dimensions. Based on a decomposition of the velocity space, these equations can be reduced to a discrete elliptic problem by eliminating the pressure through the use of substructures of the domain. The practicality of the reduction relies on a local basis, presented here, for the divergence-free subspace of the velocity space. We consider additive and multiplicative domain decomposition methods for solving the reduced elliptic problem, and their uniform convergence is established.

Stability of stationary solutions for inflow problem on the micropolar fluid model

NASA Astrophysics Data System (ADS)

Yin, Haiyan

2017-04-01

In this paper, we study the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in a half-line R+:=(0,∞). We prove that the corresponding stationary solutions of the small amplitude to the inflow problem for the micropolar fluid model are time asymptotically stable under small H1 perturbations in both the subsonic and degenerate cases. The microrotation velocity brings us some additional troubles compared with Navier-Stokes equations in the absence of the microrotation velocity. The proof of asymptotic stability is based on the basic energy method.

Fracture and contact problems for an elastic wedge

NASA Technical Reports Server (NTRS)

Erdogan, F.; Arin, K.

1974-01-01

The plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle is discussed. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

Fracture and contact problems for an elastic wedge

NASA Technical Reports Server (NTRS)

Erdogan, F.; Arin, K.

1976-01-01

The paper deals with the plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

Aeroacoustic simulation of a linear cascade by a prefactored compact scheme

NASA Astrophysics Data System (ADS)

Ghillani, Pietro

This work documents the development of a three-dimensional high-order prefactored compact finite-difference solver for computational aeroacoustics (CAA) based on the inviscid Euler equations. This time explicit scheme is applied to representative problems of sound generation by flow interacting with solid boundaries. Four aeroacoustic problems are explored and the results validated against available reference analytical solution. Selected mesh convergence studies are conducted to determine the effective order of accuracy of the complete scheme. The first test case simulates the noise emitted by a still cylinder in an oscillating field. It provides a simple validation for the CAA-compatible solid wall condition used in the remainder of the work. The following test cases are increasingly complex versions of the turbomachinery rotor-stator interaction problem taken from NASA CAA workshops. In all the cases the results are compared against the available literature. The numerical method features some appreciable contributions to computational aeroacoustics. A reduced data exchange technique for parallel computations is implemented, which requires the exchange of just two values for each boundary node, independently of the size of the zone overlap. A modified version of the non-reflecting buffer layer by Chen is used to allow aerodynamic perturbations at the through flow boundaries. The Giles subsonic boundary conditions are extended to three-dimensional curvilinear coordinates. These advances have enabled to resolve the aerodynamic noise generation and near-field propagation on a representative cascade geometry with a time-marching scheme, with accuracy similar to spectral methods..

User's guide to four-body and three-body trajectory optimization programs

NASA Technical Reports Server (NTRS)

Pu, C. L.; Edelbaum, T. N.

1974-01-01

A collection of computer programs and subroutines written in FORTRAN to calculate 4-body (sun-earth-moon-space) and 3-body (earth-moon-space) optimal trajectories is presented. The programs incorporate a variable step integration technique and a quadrature formula to correct single step errors. The programs provide capability to solve initial value problem, two point boundary value problem of a transfer from a given initial position to a given final position in fixed time, optimal 2-impulse transfer from an earth parking orbit of given inclination to a given final position and velocity in fixed time and optimal 3-impulse transfer from a given position to a given final position and velocity in fixed time.

Relaxation of an unsteady turbulent boundary layer on a flat plate in an expansion tube

NASA Technical Reports Server (NTRS)

Gurta, R. N.; Trimpi, R. L.

1974-01-01

An analysis is presented for the relaxation of a turbulent boundary layer on a semi-infinite flat plate after passage of a shock wave and a trailing driver gas-driven gas interface. The problem has special application to expansion-tube flows. The flow-governing equations have been transformed into the Crocco variables, and a time-similar solution is presented in terms of the dimensionless distance-time variable alpha and the dimensionless velocity variable beta. An eddy-viscosity model, similar to that of time-steady boundary layers, is applied to the inner and outer regions of the boundary layer. A turbulent Prandtl number equal to the molecular Prandtl number is used to relate the turbulent heat flux to the eddy viscosity. The numerical results, obtained by using the Gauss-Seidel line-relaxation method, indicate that a fully turbulent boundary layer relaxes faster to the final steady-state values of heat transfer and skin friction than a laminar boundary layer. The results also give a fairly good estimate of the local skin friction and heat transfer for near steady-flow conditions.

A finite-element analysis for steady and oscillatory supersonic flows around complex configurations

NASA Technical Reports Server (NTRS)

Morino, L.; Chen, L. T.

1974-01-01

The problem of small perturbation potential supersonic flow around complex configurations is considered. This problem requires the solution of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the small perturbation boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements, sigma sub i, which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element is assumed to be constant and equal to its value at the centroid of the element, and this yields a set of linear algebraic equations. The coefficients of the equation are given by source and doublet integrals over the surface elements, sigma sub i. The results obtained using the above formulation are compared with existing analytical and experimental results.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rehman, Nasir, E-mail: nasirzainy1@hotmail.com; Shashiashvili, Malkhaz

The classical Garman-Kohlhagen model for the currency exchange assumes that the domestic and foreign currency risk-free interest rates are constant and the exchange rate follows a log-normal diffusion process.In this paper we consider the general case, when exchange rate evolves according to arbitrary one-dimensional diffusion process with local volatility that is the function of time and the current exchange rate and where the domestic and foreign currency risk-free interest rates may be arbitrary continuous functions of time. First non-trivial problem we encounter in time-dependent case is the continuity in time argument of the value function of the American put optionmore » and the regularity properties of the optimal exercise boundary. We establish these properties based on systematic use of the monotonicity in volatility for the value functions of the American as well as European options with convex payoffs together with the Dynamic Programming Principle and we obtain certain type of comparison result for the value functions and corresponding exercise boundaries for the American puts with different strikes, maturities and volatilities.Starting from the latter fact that the optimal exercise boundary curve is left continuous with right-hand limits we give a mathematically rigorous and transparent derivation of the significant early exercise premium representation for the value function of the American foreign exchange put option as the sum of the European put option value function and the early exercise premium.The proof essentially relies on the particular property of the stochastic integral with respect to arbitrary continuous semimartingale over the predictable subsets of its zeros. We derive from the latter the nonlinear integral equation for the optimal exercise boundary which can be studied by numerical methods.« less

Assessing the applicability of WRF optimal parameters under the different precipitation simulations in the Greater Beijing Area

NASA Astrophysics Data System (ADS)

Di, Zhenhua; Duan, Qingyun; Wang, Chen; Ye, Aizhong; Miao, Chiyuan; Gong, Wei

2018-03-01

Forecasting skills of the complex weather and climate models have been improved by tuning the sensitive parameters that exert the greatest impact on simulated results based on more effective optimization methods. However, whether the optimal parameter values are still work when the model simulation conditions vary, which is a scientific problem deserving of study. In this study, a highly-effective optimization method, adaptive surrogate model-based optimization (ASMO), was firstly used to tune nine sensitive parameters from four physical parameterization schemes of the Weather Research and Forecasting (WRF) model to obtain better summer precipitation forecasting over the Greater Beijing Area in China. Then, to assess the applicability of the optimal parameter values, simulation results from the WRF model with default and optimal parameter values were compared across precipitation events, boundary conditions, spatial scales, and physical processes in the Greater Beijing Area. The summer precipitation events from 6 years were used to calibrate and evaluate the optimal parameter values of WRF model. Three boundary data and two spatial resolutions were adopted to evaluate the superiority of the calibrated optimal parameters to default parameters under the WRF simulations with different boundary conditions and spatial resolutions, respectively. Physical interpretations of the optimal parameters indicating how to improve precipitation simulation results were also examined. All the results showed that the optimal parameters obtained by ASMO are superior to the default parameters for WRF simulations for predicting summer precipitation in the Greater Beijing Area because the optimal parameters are not constrained by specific precipitation events, boundary conditions, and spatial resolutions. The optimal values of the nine parameters were determined from 127 parameter samples using the ASMO method, which showed that the ASMO method is very highly-efficient for optimizing WRF model parameters.

Scalar Casimir densities and forces for parallel plates in cosmic string spacetime

NASA Astrophysics Data System (ADS)

Bezerra de Mello, E. R.; Saharian, A. A.; Abajyan, S. V.

2018-04-01

We analyze the Green function, the Casimir densities and forces associated with a massive scalar quantum field confined between two parallel plates in a higher dimensional cosmic string spacetime. The plates are placed orthogonal to the string, and the field obeys the Robin boundary conditions on them. The boundary-induced contributions are explicitly extracted in the vacuum expectation values (VEVs) of the field squared and of the energy-momentum tensor for both the single plate and two plates geometries. The VEV of the energy-momentum tensor, in additional to the diagonal components, contains an off diagonal component corresponding to the shear stress. The latter vanishes on the plates in special cases of Dirichlet and Neumann boundary conditions. For points outside the string core the topological contributions in the VEVs are finite on the plates. Near the string the VEVs are dominated by the boundary-free part, whereas at large distances the boundary-induced contributions dominate. Due to the nonzero off diagonal component of the vacuum energy-momentum tensor, in addition to the normal component, the Casimir forces have nonzero component parallel to the boundary (shear force). Unlike the problem on the Minkowski bulk, the normal forces acting on the separate plates, in general, do not coincide if the corresponding Robin coefficients are different. Another difference is that in the presence of the cosmic string the Casimir forces for Dirichlet and Neumann boundary conditions differ. For Dirichlet boundary condition the normal Casimir force does not depend on the curvature coupling parameter. This is not the case for other boundary conditions. A new qualitative feature induced by the cosmic string is the appearance of the shear stress acting on the plates. The corresponding force is directed along the radial coordinate and vanishes for Dirichlet and Neumann boundary conditions. Depending on the parameters of the problem, the radial component of the shear force can be either positive or negative.

Steady-state groundwater recharge in trapezoidal-shaped aquifers: A semi-analytical approach based on variational calculus

NASA Astrophysics Data System (ADS)

Mahdavi, Ali; Seyyedian, Hamid

2014-05-01

This study presents a semi-analytical solution for steady groundwater flow in trapezoidal-shaped aquifers in response to an areal diffusive recharge. The aquifer is homogeneous, anisotropic and interacts with four surrounding streams of constant-head. Flow field in this laterally bounded aquifer-system is efficiently constructed by means of variational calculus. This is accomplished by minimizing a properly defined penalty function for the associated boundary value problem. Simple yet demonstrative scenarios are defined to investigate anisotropy effects on the water table variation. Qualitative examination of the resulting equipotential contour maps and velocity vector field illustrates the validity of the method, especially in the vicinity of boundary lines. Extension to the case of triangular-shaped aquifer with or without an impervious boundary line is also demonstrated through a hypothetical example problem. The present solution benefits from an extremely simple mathematical expression and exhibits strictly close agreement with the numerical results obtained from Modflow. Overall, the solution may be used to conduct sensitivity analysis on various hydrogeological parameters that affect water table variation in aquifers defined in trapezoidal or triangular-shaped domains.

Research on the Automatic Fusion Strategy of Fixed Value Boundary Based on the Weak Coupling Condition of Grid Partition

NASA Astrophysics Data System (ADS)

Wang, X. Y.; Dou, J. M.; Shen, H.; Li, J.; Yang, G. S.; Fan, R. Q.; Shen, Q.

2018-03-01

With the continuous strengthening of power grids, the network structure is becoming more and more complicated. An open and regional data modeling is used to complete the calculation of the protection fixed value based on the local region. At the same time, a high precision, quasi real-time boundary fusion technique is needed to seamlessly integrate the various regions so as to constitute an integrated fault computing platform which can conduct transient stability analysis of covering the whole network with high accuracy and multiple modes, deal with the impact results of non-single fault, interlocking fault and build “the first line of defense” of the power grid. The boundary fusion algorithm in this paper is an automatic fusion algorithm based on the boundary accurate coupling of the networking power grid partition, which takes the actual operation mode for qualification, complete the boundary coupling algorithm of various weak coupling partition based on open-loop mode, improving the fusion efficiency, truly reflecting its transient stability level, and effectively solving the problems of too much data, too many difficulties of partition fusion, and no effective fusion due to mutually exclusive conditions. In this paper, the basic principle of fusion process is introduced firstly, and then the method of boundary fusion customization is introduced by scene description. Finally, an example is given to illustrate the specific algorithm on how it effectively implements the boundary fusion after grid partition and to verify the accuracy and efficiency of the algorithm.

Flow of “stress power-law” fluids between parallel rotating discs with distinct axes

DOE PAGES

Srinivasan, Shriram; Karra, Satish

2015-04-16

The problem of flow between parallel rotating discs with distinct axes corresponds to the case of flow in an orthogonal rheometer and has been studied extensively for different fluids since the instrument's inception. All the prior studies presume a constitutive prescription of the fluid stress in terms of the kinematical variables. In this paper, we approach the problem from a different perspective, i.e., a constitutive specification of the symmetric part of the velocity gradient in terms of the Cauchy stress. Such an approach ensures that the boundary conditions can be incorporated in a manner quite faithful to real world experimentsmore » with the instrument. Interestingly, the choice of the boundary condition is critical to the solvability of the problem for the case of creeping/Stokes flow. Furthermore, when the no-slip condition is enforced at the boundaries, depending on the model parameters and axes offset, the fluid response can show non-uniqueness or unsolvability, features which are absent in a conventional constitutive specification. In case of creeping/Stokes flow with prescribed values of the stress, the fluid response is indeterminate. We also record the response of a particular case of the given “stress power-law” fluid; one that cannot be attained by the conventional power-law fluids.« less

Correction of Excessive Precipitation Over Steep and High Mountains in a General Circulation Model

NASA Technical Reports Server (NTRS)

Chao, Winston C.

2012-01-01

Excessive precipitation over steep and high mountains (EPSM) is a well-known problem in GCMs and meso-scale models. This problem impairs simulation and data assimilation products. Among the possible causes investigated in this study, we found that the most important one, by far, is a missing upward transport of heat out of the boundary layer due to the vertical circulations forced by the daytime upslope winds, which are forced by the heated boundary layer on subgrid-scale slopes. These upslope winds are associated with large subgrid-scale topographic variation, which is found over steep and high mountains. Without such subgridscale heat ventilation, the resolvable-scale upslope flow in the boundary layer generated by surface sensible heat flux along the mountain slopes is excessive. Such an excessive resolvablescale upslope flow combined with the high moisture content in the boundary layer results in excessive moisture transport toward mountaintops, which in turn gives rise to EPSM. Other possible causes of EPSM that we have investigated include 1) a poorly-designed horizontal moisture flux in the terrain-following coordinates, 2) the condition for cumulus convection being too easily satisfied at mountaintops, 3) the presence of conditional instability of the computational kind, and 4) the absence of blocked flow drag. These are all minor or inconsequential. We have parameterized the ventilation effects of the subgrid-scale heated-slope-induced vertical circulation (SHVC) by removing heat from the boundary layer and depositing it in layers higher up when the topographic variance exceeds a critical value. Test results using NASA/Goddard's GEOS-S GCM have shown that this largely solved the EPSM problem.

Numerical Solution of Systems of Loaded Ordinary Differential Equations with Multipoint Conditions

NASA Astrophysics Data System (ADS)

Assanova, A. T.; Imanchiyev, A. E.; Kadirbayeva, Zh. M.

2018-04-01

A system of loaded ordinary differential equations with multipoint conditions is considered. The problem under study is reduced to an equivalent boundary value problem for a system of ordinary differential equations with parameters. A system of linear algebraic equations for the parameters is constructed using the matrices of the loaded terms and the multipoint condition. The conditions for the unique solvability and well-posedness of the original problem are established in terms of the matrix made up of the coefficients of the system of linear algebraic equations. The coefficients and the righthand side of the constructed system are determined by solving Cauchy problems for linear ordinary differential equations. The solutions of the system are found in terms of the values of the desired function at the initial points of subintervals. The parametrization method is numerically implemented using the fourth-order accurate Runge-Kutta method as applied to the Cauchy problems for ordinary differential equations. The performance of the constructed numerical algorithms is illustrated by examples.

Nonlinear Wave Propagation

DTIC Science & Technology

1989-05-22

multidimensional systems of physi- cal significance. Prototypes are the Kadomtsev - Petviashvili and Davey-Stewartson equations . The nature of the boundary value...Ono equation bears many similarities to multidimensional problems, specifically the Kadomtsev - Petviashvili equation . In some sense the nonlocality...Inverse scattering and Direct Linearizing Transforms for the Kadomtsev - Petviashvili Equations , A.S. Fokas, and M.J. Ablowitz, Phys. Lett. Vol., 94A, No. 2

Highly Accurate Beam Torsion Solutions Using the p-Version Finite Element Method

NASA Technical Reports Server (NTRS)

Smith, James P.

1996-01-01

A new treatment of the classical beam torsion boundary value problem is applied. Using the p-version finite element method with shape functions based on Legendre polynomials, torsion solutions for generic cross-sections comprised of isotropic materials are developed. Element shape functions for quadrilateral and triangular elements are discussed, and numerical examples are provided.

A Gaussian Mixture Model-based continuous Boundary Detection for 3D sensor networks.

PubMed

Chen, Jiehui; Salim, Mariam B; Matsumoto, Mitsuji

2010-01-01

This paper proposes a high precision Gaussian Mixture Model-based novel Boundary Detection 3D (BD3D) scheme with reasonable implementation cost for 3D cases by selecting a minimum number of Boundary sensor Nodes (BNs) in continuous moving objects. It shows apparent advantages in that two classes of boundary and non-boundary sensor nodes can be efficiently classified using the model selection techniques for finite mixture models; furthermore, the set of sensor readings within each sensor node's spatial neighbors is formulated using a Gaussian Mixture Model; different from DECOMO [1] and COBOM [2], we also formatted a BN Array with an additional own sensor reading to benefit selecting Event BNs (EBNs) and non-EBNs from the observations of BNs. In particular, we propose a Thick Section Model (TSM) to solve the problem of transition between 2D and 3D. It is verified by simulations that the BD3D 2D model outperforms DECOMO and COBOM in terms of average residual energy and the number of BNs selected, while the BD3D 3D model demonstrates sound performance even for sensor networks with low densities especially when the value of the sensor transmission range (r) is larger than the value of Section Thickness (d) in TSM. We have also rigorously proved its correctness for continuous geometric domains and full robustness for sensor networks over 3D terrains.

Adaptive Framework for Classification and Novel Class Detection over Evolving Data Streams with Limited Labeled Data.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haque, Ahsanul; Khan, Latifur; Baron, Michael

2015-09-01

Most approaches to classifying evolving data streams either divide the stream of data into fixed-size chunks or use gradual forgetting to address the problems of infinite length and concept drift. Finding the fixed size of the chunks or choosing a forgetting rate without prior knowledge about time-scale of change is not a trivial task. As a result, these approaches suffer from a trade-off between performance and sensitivity. To address this problem, we present a framework which uses change detection techniques on the classifier performance to determine chunk boundaries dynamically. Though this framework exhibits good performance, it is heavily dependent onmore » the availability of true labels of data instances. However, labeled data instances are scarce in realistic settings and not readily available. Therefore, we present a second framework which is unsupervised in nature, and exploits change detection on classifier confidence values to determine chunk boundaries dynamically. In this way, it avoids the use of labeled data while still addressing the problems of infinite length and concept drift. Moreover, both of our proposed frameworks address the concept evolution problem by detecting outliers having similar values for the attributes. We provide theoretical proof that our change detection method works better than other state-of-the-art approaches in this particular scenario. Results from experiments on various benchmark and synthetic data sets also show the efficiency of our proposed frameworks.« less

A fast and accurate imaging algorithm in optical/diffusion tomography

NASA Astrophysics Data System (ADS)

Klibanov, M. V.; Lucas, T. R.; Frank, R. M.

1997-10-01

An n-dimensional (n = 2,3) inverse problem for the parabolic/diffusion equation 0266-5611/13/5/015/img1, 0266-5611/13/5/015/img2, 0266-5611/13/5/015/img3, 0266-5611/13/5/015/img4 is considered. The problem consists of determining the function a(x) inside of a bounded domain 0266-5611/13/5/015/img5 given the values of the solution u(x,t) for a single source location 0266-5611/13/5/015/img6 on a set of detectors 0266-5611/13/5/015/img7, where 0266-5611/13/5/015/img8 is the boundary of 0266-5611/13/5/015/img9. A novel numerical method is derived and tested. Numerical tests are conducted for n = 2 and for ranges of parameters which are realistic for applications to early breast cancer diagnosis and the search for mines in murky shallow water using ultrafast laser pulses. The main innovation of this method lies in a new approach for a novel linearized problem (LP). Such a LP is derived and reduced to a well-posed boundary-value problem for a coupled system of elliptic partial differential equations. A principal advantage of this technique is in its speed and accuracy, since it leads to the factorization of well conditioned, sparse matrices with non-zero entries clustered in a narrow band near the diagonal. The authors call this approach the elliptic systems method (ESM). The ESM can be extended to other imaging modalities.

Oracle estimation of parametric models under boundary constraints.

PubMed

Wong, Kin Yau; Goldberg, Yair; Fine, Jason P

2016-12-01

In many classical estimation problems, the parameter space has a boundary. In most cases, the standard asymptotic properties of the estimator do not hold when some of the underlying true parameters lie on the boundary. However, without knowledge of the true parameter values, confidence intervals constructed assuming that the parameters lie in the interior are generally over-conservative. A penalized estimation method is proposed in this article to address this issue. An adaptive lasso procedure is employed to shrink the parameters to the boundary, yielding oracle inference which adapt to whether or not the true parameters are on the boundary. When the true parameters are on the boundary, the inference is equivalent to that which would be achieved with a priori knowledge of the boundary, while if the converse is true, the inference is equivalent to that which is obtained in the interior of the parameter space. The method is demonstrated under two practical scenarios, namely the frailty survival model and linear regression with order-restricted parameters. Simulation studies and real data analyses show that the method performs well with realistic sample sizes and exhibits certain advantages over standard methods. © 2016, The International Biometric Society.

Stability investigations of airfoil flow by global analysis

NASA Technical Reports Server (NTRS)

Morzynski, Marek; Thiele, Frank

1992-01-01

As the result of global, non-parallel flow stability analysis the single value of the disturbance growth-rate and respective frequency is obtained. This complex value characterizes the stability of the whole flow configuration and is not referred to any particular flow pattern. The global analysis assures that all the flow elements (wake, boundary and shear layer) are taken into account. The physical phenomena connected with the wake instability are properly reproduced by the global analysis. This enhances the investigations of instability of any 2-D flows, including ones in which the boundary layer instability effects are known to be of dominating importance. Assuming fully 2-D disturbance form, the global linear stability problem is formulated. The system of partial differential equations is solved for the eigenvalues and eigenvectors. The equations, written in the pure stream function formulation, are discretized via FDM using a curvilinear coordinate system. The complex eigenvalues and corresponding eigenvectors are evaluated by an iterative method. The investigations performed for various Reynolds numbers emphasize that the wake instability develops into the Karman vortex street. This phenomenon is shown to be connected with the first mode obtained from the non-parallel flow stability analysis. The higher modes are reflecting different physical phenomena as for example Tollmien-Schlichting waves, originating in the boundary layer and having the tendency to emerge as instabilities for the growing Reynolds number. The investigations are carried out for a circular cylinder, oblong ellipsis and airfoil. It is shown that the onset of the wake instability, the waves in the boundary layer, the shear layer instability are different solutions of the same eigenvalue problem, formulated using the non-parallel theory. The analysis offers large potential possibilities as the generalization of methods used till now for the stability analysis.

Higher modes of the Orr-Sommerfeld problem for boundary layer flows

NASA Technical Reports Server (NTRS)

Lakin, W. D.; Grosch, C. E.

1983-01-01

The discrete spectrum of the Orr-Sommerfeld problem of hydrodynamic stability for boundary layer flows in semi-infinite regions is examined. Related questions concerning the continuous spectrum are also addressed. Emphasis is placed on the stability problem for the Blasius boundary layer profile. A general theoretical result is given which proves that the discrete spectrum of the Orr-Sommerfeld problem for boundary layer profiles (U(y), 0,0) has only a finite number of discrete modes when U(y) has derivatives of all orders. Details are given of a highly accurate numerical technique based on collocation with splines for the calculation of stability characteristics. The technique includes replacement of 'outer' boundary conditions by asymptotic forms based on the proper large parameter in the stability problem. Implementation of the asymptotic boundary conditions is such that there is no need to make apriori distinctions between subcases of the discrete spectrum or between the discrete and continuous spectrums. Typical calculations for the usual Blasius problem are presented.

Some Recent Contributions to the Study of Transition and Turbulent Boundary Layers

NASA Technical Reports Server (NTRS)

Dryden, Hugh L

1947-01-01

The first part of this paper reviews the present state of the problem of the instability of laminar boundary layers which has formed an important part of the general lectures by von Karman at the first and fourth Congresses and by Taylor at the fifth Congress. This problem may now be considered as essentially solved as the result of work completed since 1938. When the velocity fluctuations of the free-stream flow are less than 0.1 percent of the mean speed, instability occurs as described by the well-known Tollmien-Schlichting theory. The Tollmien-Schlichting waves were first observed experimentally by Schubauer and Skramstad in 1940. They devised methods of introducing controlled small disturbances and obtained measured values of frequency, damping, and wave length at various Reynolds numbers which agreed well with the theoretical results. Their experimental results were confirmed by Liepmann. Much theoretical work was done in Germany in extending the Tol1mien-Schlichting theory to other boundary conditions, in particular to flow along a porous wall to which suction is applied for removing part of the boundary layer. The second part of this paper summarizes the present state of knowledge of the mechanics of turbulent boundary layers, and of the methods now being used for fundamental studies of the turbulent fluctuations in turbulent boundary layers. A brief review is given of the semi-empirical method of approach as developed by Buri, Gruschwitz, Fediaevsky, and Kalikhman. In recent years the National Advisory.Commsittee for Aeronautics has sponsored a detailed study at the National Bureau of Standards of the turbulent fluctuations in a turbulent boundary layer under adverse pressure gradient sufficient to produce separation. The aims of this investigation and its present status are described.

TORO II: A finite element computer program for nonlinear quasi-static problems in electromagnetics: Part 1, Theoretical background

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gartling, D.K.

The theoretical and numerical background for the finite element computer program, TORO II, is presented in detail. TORO II is designed for the multi-dimensional analysis of nonlinear, electromagnetic field problems described by the quasi-static form of Maxwell`s equations. A general description of the boundary value problems treated by the program is presented. The finite element formulation and the associated numerical methods used in TORO II are also outlined. Instructions for the use of the code are documented in SAND96-0903; examples of problems analyzed with the code are also provided in the user`s manual. 24 refs., 8 figs.

A note on the problem of choosing a model of the universe. II

NASA Astrophysics Data System (ADS)

Skalsky, Vladimir

1989-05-01

The value of the mean mass density (rho) of the universe is examined. It is shown that there is a difference between the present terrestrial conditions and the initial conditions of the universe expansion and that, for the sphere of the physical boundary conditions represented by Planck's values (when the present evolution phase of the universe was probably decided), there are serious limitations for the value of rho. It is postulated on the basis of these limiting conditions that some cause may exist for which the condition corresponding to the critical mass density of the universe was realized.

Chandrasekhar-type algorithms for fast recursive estimation in linear systems with constant parameters

NASA Technical Reports Server (NTRS)

Choudhury, A. K.; Djalali, M.

1975-01-01

In this recursive method proposed, the gain matrix for the Kalman filter and the convariance of the state vector are computed not via the Riccati equation, but from certain other equations. These differential equations are of Chandrasekhar-type. The 'invariant imbedding' idea resulted in the reduction of the basic boundary value problem of transport theory to an equivalent initial value system, a significant computational advance. Initial value experience showed that there is some computational savings in the method and the loss of positive definiteness of the covariance matrix is less vulnerable.

Thermal Convection in a Creeping Solid With Melting/Freezing Interfaces at Either or Both Boundaries

NASA Astrophysics Data System (ADS)

Labrosse, S.; Morison, A.; Deguen, R.; Alboussiere, T.; Tackley, P. J.; Agrusta, R.

2017-12-01

Thermal convection in the solid mantles of the Earth, other terrestrial planets and icy satellites sets in while it is still crystallising from a liquid layer (see abstract by Morison et al, this conference). The existence of an ocean (water or magma) either or both below and above the solid mantle modifies the conditions applying at the boundary since matter can flow through it by changing phase. Adapting the boundary conditions developed for the dynamics of the inner core by Deguen et al (GJI 2013) to the plane layer and the spherical shell, we solve the linear stability problem and obtain weakly non-linear solutions as well as direct numerical solutions in both geometries, with a liquid-solid phase change at either or both boundaries. The phase change boundary condition is controlled by a dimensionless number, Φ , which when small, allows easy flow through the boundary while the classical non-penetrating boundary condition is recovered for large values. If both boundaries have a phase change, the preferred wavelength of the flow is large, i.e. λ ∝Φ -1/2 in a plane layer and degree 1 in a spherical shell, and the critical Rayleigh number is of order Φ . The heat transfer efficiency, as measured by the dependence of the Nusselt number on the Rayleigh number also increases indefinitely for decreasing values of Φ . If only one boundary has a phase change condition, the critical wavelength is increased by about a factor 2 and the critical Rayleigh number is decreased by about a factor 4. The dynamics is controlled entirely by the boundary layer opposite to the phase change interface and the geometry of the flow. This model provides a natural explanation for the emergence of degree 1 convection in thin ice layers and implies a style of early mantle dynamics on Earth very different from what is classically envisioned.

On the Possibility of Estimation of the Earth Crust's Properties from the Observations of Electric Field of Electrokinetic Origin, Generated by Tidal Deformation within the Fault Zone

NASA Astrophysics Data System (ADS)

Alekseev, D. A.; Gokhberg, M. B.

2018-05-01

A 2-D boundary problem formulation in terms of pore pressure in Biot poroelasticity model is discussed, with application to a vertical contact model mechanically excited by a lunar-solar tidal deformation wave, representing a fault zone structure. A problem parametrization in terms of permeability and Biot's modulus contrasts is proposed and its numerical solution is obtained for a series of models differing in the values of the above parameters. The behavior of pore pressure and its gradient is analyzed. From those, the electric field of the electrokinetic nature is calculated. The possibilities of estimation of the elastic properties and permeability of geological formations from the observations of the horizontal and vertical electric field measured inside the medium and at the earth's surface near the block boundary are discussed.

Study of a mixed dispersal population dynamics model

DOE PAGES

Chugunova, Marina; Jadamba, Baasansuren; Kao, Chiu -Yen; ...

2016-08-27

In this study, we consider a mixed dispersal model with periodic and Dirichlet boundary conditions and its corresponding linear eigenvalue problem. This model describes the time evolution of a population which disperses both locally and non-locally. We investigate how long time dynamics depend on the parameter values. Furthermore, we study the minimization of the principal eigenvalue under the constraints that the resource function is bounded from above and below, and with a fixed total integral. Biologically, this minimization problem is motivated by the question of determining the optimal spatial arrangement of favorable and unfavorable regions for the species to diemore » out more slowly or survive more easily. Our numerical simulations indicate that the optimal favorable region tends to be a simply-connected domain. Numerous results are shown to demonstrate various scenarios of optimal favorable regions for periodic and Dirichlet boundary conditions.« less

A computer program to trace seismic ray distribution in complex two-dimensional geological models

USGS Publications Warehouse

Yacoub, Nazieh K.; Scott, James H.

1970-01-01

A computer program has been developed to trace seismic rays and their amplitudes and energies through complex two-dimensional geological models, for which boundaries between elastic units are defined by a series of digitized X-, Y-coordinate values. Input data for the program includes problem identification, control parameters, model coordinates and elastic parameter for the elastic units. The program evaluates the partitioning of ray amplitude and energy at elastic boundaries, computes the total travel time, total travel distance and other parameters for rays arising at the earth's surface. Instructions are given for punching program control cards and data cards, and for arranging input card decks. An example of printer output for a simple problem is presented. The program is written in FORTRAN IV language. The listing of the program is shown in the Appendix, with an example output from a CDC-6600 computer.

A non-local free boundary problem arising in a theory of financial bubbles

PubMed Central

Berestycki, Henri; Monneau, Regis; Scheinkman, José A.

2014-01-01

We consider an evolution non-local free boundary problem that arises in the modelling of speculative bubbles. The solution of the model is the speculative component in the price of an asset. In the framework of viscosity solutions, we show the existence and uniqueness of the solution. We also show that the solution is convex in space, and establish several monotonicity properties of the solution and of the free boundary with respect to parameters of the problem. To study the free boundary, we use, in particular, the fact that the odd part of the solution solves a more standard obstacle problem. We show that the free boundary is and describe the asymptotics of the free boundary as c, the cost of transacting the asset, goes to zero. PMID:25288815

Sound-structure interaction analysis of an infinite-long cylindrical shell submerged in a quarter water domain and subject to a line-distributed harmonic excitation

NASA Astrophysics Data System (ADS)

Guo, Wenjie; Li, Tianyun; Zhu, Xiang; Miao, Yuyue

2018-05-01

The sound-structure coupling problem of a cylindrical shell submerged in a quarter water domain is studied. A semi-analytical method based on the double wave reflection method and the Graf's addition theorem is proposed to solve the vibration and acoustic radiation of an infinite cylindrical shell excited by an axially uniform harmonic line force, in which the acoustic boundary conditions consist of a free surface and a vertical rigid surface. The influences of the complex acoustic boundary conditions on the vibration and acoustic radiation of the cylindrical shell are discussed. It is found that the complex acoustic boundary has crucial influence on the vibration of the cylindrical shell when the cylindrical shell approaches the boundary, and the influence tends to vanish when the distances between the cylindrical shell and the boundaries exceed certain values. However, the influence of the complex acoustic boundary on the far-field sound pressure of the cylindrical shell cannot be ignored. The far-field acoustic directivity of the cylindrical shell varies with the distances between the cylindrical shell and the boundaries, besides the driving frequency. The work provides more understanding on the vibration and acoustic radiation behaviors of cylindrical shells with complex acoustic boundary conditions.

Viscous Forces in Velocity Boundary Layers around Planetary Ionospheres.

PubMed

Pérez-De-Tejada

1999-11-01

A discussion is presented to examine the role of viscous forces in the transport of solar wind momentum to the ionospheric plasma of weakly magnetized planets (Venus and Mars). Observational data are used to make a comparison of the Reynolds and Maxwell stresses that are operative in the interaction of the solar wind with local plasma (planetary ionospheres). Measurements show the presence of a velocity boundary layer formed around the flanks of the ionosphere where the shocked solar wind has reached super-Alfvénic speeds. It is found that the Reynolds stresses in the solar wind at that region can be larger than the Maxwell stresses and thus are necessary in the local acceleration of the ionospheric plasma. From an order-of-magnitude calculation of the Reynolds stresses, it is possible to derive values of the kinematic viscosity and the Reynolds number that are suitable to the gyrotropic motion of the solar wind particles across the boundary layer. The value of the kinematic viscosity is comparable to those inferred from studies of the transport of solar wind momentum to the earth's magnetosphere and thus suggest a common property of the solar wind around planetary obstacles. Similar conditions could also be applicable to velocity boundary layers formed in other plasma interaction problems in astrophysics.

On the Problem of Filtration to an Imperfect Gallery in a Pressureless Bed

NASA Astrophysics Data System (ADS)

Bereslavskii, É. N.; Dudina, L. M.

2018-01-01

The problem of plane steady-state filtration in a pressureless bed to an imperfect gallery in the presence of evaporation from the flow free surface is considered. To study such type of flow, a mixed boundary-value problem of the theory of analytical functions is formulated and solved with application of the Polubarinova-Kochina method. Based on the model suggested, an algorithm for computing the discharge of the gallery and the ordinate of free surface emergence to the impermeable screen is developed. A detailed hydrodynamic analysis of the influence of all physical parameters of the model on the desired filtration characteristics is given.

An exact stiffness theory for unidirectional xFRP composites

NASA Astrophysics Data System (ADS)

Klasztorny, M.; Konderla, P.; Piekarski, R.

2009-01-01

UD xFRP composites, i.e., isotropic plastics reinforced with long transversely isotropic fibres packed unidirectionally according to the hexagonal scheme are considered. The constituent materials are geometrically and physically linear. The previous formulations of the exact stiffness theory of such composites are revised, and the theory is developed further based on selected boundary-value problems of elasticity theory. The numerical examples presented are focussed on testing the theory with account of previous variants of this theory and experimental values of the effective elastic constants. The authors have pointed out that the exact stiffness theory of UD xFRP composites, with the modifications proposed in our study, will be useful in the engineering practice and in solving the current problems of the mechanics of composite materials.

Girsanov's transformation based variance reduced Monte Carlo simulation schemes for reliability estimation in nonlinear stochastic dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kanjilal, Oindrila, E-mail: oindrila@civil.iisc.ernet.in; Manohar, C.S., E-mail: manohar@civil.iisc.ernet.in

The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the secondmore » explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations. - Highlights: • The distance minimizing control forces minimize a bound on the sampling variance. • Establishing Girsanov controls via solution of a two-point boundary value problem. • Girsanov controls via Volterra's series representation for the transfer functions.« less

Force-free magnetic fields - The magneto-frictional method

NASA Technical Reports Server (NTRS)

Yang, W. H.; Sturrock, P. A.; Antiochos, S. K.

1986-01-01

The problem under discussion is that of calculating magnetic field configurations in which the Lorentz force j x B is everywhere zero, subject to specified boundary conditions. We choose to represent the magnetic field in terms of Clebsch variables in the form B = grad alpha x grad beta. These variables are constant on any field line so that each field line is labeled by the corresponding values of alpha and beta. When the field is described in this way, the most appropriate choice of boundary conditions is to specify the values of alpha and beta on the bounding surface. We show that such field configurations may be calculated by a magneto-frictional method. We imagine that the field lines move through a stationary medium, and that each element of magnetic field is subject to a frictional force parallel to and opposing the velocity of the field line. This concept leads to an iteration procedure for modifying the variables alpha and beta, that tends asymptotically towards the force-free state. We apply the method first to a simple problem in two rectangular dimensions, and then to a problem of cylindrical symmetry that was previously discussed by Barnes and Sturrock (1972). In one important respect, our new results differ from the earlier results of Barnes and Sturrock, and we conclude that the earlier article was in error.

A Source-Term Based Boundary Layer Bleed/Effusion Model for Passive Shock Control

NASA Technical Reports Server (NTRS)

Baurle, Robert A.; Norris, Andrew T.

2011-01-01

A modeling framework for boundary layer effusion has been developed based on the use of source (or sink) terms instead of the usual practice of specifying bleed directly as a boundary condition. This framework allows the surface boundary condition (i.e. isothermal wall, adiabatic wall, slip wall, etc.) to remain unaltered in the presence of bleed. This approach also lends itself to easily permit the addition of empirical models for second order effects that are not easily accounted for by simply defining effective transpiration values. Two effusion models formulated for supersonic flows have been implemented into this framework; the Doerffer/Bohning law and the Slater formulation. These models were applied to unit problems that contain key aspects of the flow physics applicable to bleed systems designed for hypersonic air-breathing propulsion systems. The ability of each model to predict bulk bleed properties was assessed, as well as the response of the boundary layer as it passes through and downstream of a porous bleed system. The model assessment was performed with and without the presence of shock waves. Three-dimensional CFD simulations that included the geometric details of the porous plate bleed systems were also carried out to supplement the experimental data, and provide additional insights into the bleed flow physics. Overall, both bleed formulations fared well for the tests performed in this study. However, the sample of test problems considered in this effort was not large enough to permit a comprehensive validation of the models.

A Tensor-Train accelerated solver for integral equations in complex geometries

NASA Astrophysics Data System (ADS)

Corona, Eduardo; Rahimian, Abtin; Zorin, Denis

2017-04-01

We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical compression and inversion scheme for matrices arising from the discretization of integral equations. For a broad range of problems, computational and storage costs of the inversion scheme are extremely modest O (log ⁡ N) and once the inverse is computed, it can be applied in O (Nlog ⁡ N) . We analyze the QTT ranks for hierarchically low rank matrices and discuss its relationship to commonly used hierarchical compression techniques such as FMM and HSS. We prove that the QTT ranks are bounded for translation-invariant systems and argue that this behavior extends to non-translation invariant volume and boundary integrals. For volume integrals, the QTT decomposition provides an efficient direct solver requiring significantly less memory compared to other fast direct solvers. We present results demonstrating the remarkable performance of the QTT-based solver when applied to both translation and non-translation invariant volume integrals in 3D. For boundary integral equations, we demonstrate that using a QTT decomposition to construct preconditioners for a Krylov subspace method leads to an efficient and robust solver with a small memory footprint. We test the QTT preconditioners in the iterative solution of an exterior elliptic boundary value problem (Laplace) formulated as a boundary integral equation in complex, multiply connected geometries.

Using Literature and Innovative Assessments to Ignite Interest and Cultivate Critical Thinking Skills in an Undergraduate Neuroscience Course

ERIC Educational Resources Information Center

Lynd-Balta, Eileen

2006-01-01

Science education reform initiatives emphasize (1) the value of concepts over facts; (2) the benefits of open-ended, inquiry-based problem-solving rather than protocols leading to a single correct answer; and (3) the importance of a multidisciplinary approach to teaching that is not confined by departmental boundaries. Neuroscientists should be at…

Stabilization in a two-species chemotaxis system with a logistic source

NASA Astrophysics Data System (ADS)

Tello, J. I.; Winkler, M.

2012-05-01

We study a system of three partial differential equations modelling the spatio-temporal behaviour of two competitive populations of biological species both of which are attracted chemotactically by the same signal substance. More precisely, we consider the initial-boundary value problem for \\[ \\begin{equation*} \\fl\\left\\{ \\begin{array}{@{}l} u_t= d_1\\Delta u - \\chi_1 \

The Toda lattice as a forced integrable system

NASA Technical Reports Server (NTRS)

Hansen, P. J.; Kaup, D. J.

1985-01-01

The analytic properties of the Jost functions for the inverse scattering transform associated with the forced Toda lattice are shown to determine the time evolution of this particular boundary value problem. It is suggested that inverse scattering methods may be used generally to analyze forced integrable systems. Thus an extension of the applicability of the inverse scattering transform is indicated.

Guidance and control strategies for aerospace vehicles

NASA Technical Reports Server (NTRS)

Naidu, Desineni S.; Hibey, Joseph L.

1988-01-01

The optimal control problem arising in coplanar, orbital transfer employing aeroassist technology is addressed. The maneuver involves the transfer from high Earth orbit to low Earth orbit. A performance index is chosen the minimize the fuel consumpltion for the transfer. Simulations are carried out for establishing a corridor of entry conditions which are suitable for flying the spacecraft through the atmosphere. A highlight of the paper is the application of an efficient multiple shooting method for taming the notorious nonlinear, two-point, boundary value problem resulting from optimization procedure.

Drag Minimization for Wings and Bodies in Supersonic Flow

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Fuller, Franklyn B

1958-01-01

The minimization of inviscid fluid drag is studied for aerodynamic shapes satisfying the conditions of linearized theory, and subject to imposed constraints on lift, pitching moment, base area, or volume. The problem is transformed to one of determining two-dimensional potential flows satisfying either Laplace's or Poisson's equations with boundary values fixed by the imposed conditions. A general method for determining integral relations between perturbation velocity components is developed. This analysis is not restricted in application to optimum cases; it may be used for any supersonic wing problem.

Une formulation variationnelle du problème de contact avec frottement de Coulomb

NASA Astrophysics Data System (ADS)

Le van, Anh; Nguyen, Tai H. T.

2008-07-01

A variational relationship is proposed as the weak form of the large deformation contact problem with Coulomb friction. It is a mixed relationship involving both the displacements and the multipliers; the weighting functions are the virtual displacements and the virtual multipliers. It is shown that the proposed weak form is equivalent to the strong form of the initial/boundary value contact problem and the multipliers are equal to the contact tractions. To cite this article: A. Le van, T.H.T. Nguyen, C. R. Mecanique 336 (2008).

Analysis and Development of Finite Element Methods for the Study of Nonlinear Thermomechanical Behavior of Structural Components

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley

1995-01-01

Underintegrated methods are investigated with respect to their stability and convergence properties. The focus was on identifying regions where they work and regions where techniques such as hourglass viscosity and hourglass control can be used. Results obtained show that underintegrated methods typically lead to finite element stiffness with spurious modes in the solution. However, problems exist (scalar elliptic boundary value problems) where underintegrated with hourglass control yield convergent solutions. Also, stress averaging in underintegrated stiffness calculations does not necessarily lead to stable or convergent stress states.

The validation of a generalized Hooke's law for coronary arteries.

PubMed

Wang, Chong; Zhang, Wei; Kassab, Ghassan S

2008-01-01

The exponential form of constitutive model is widely used in biomechanical studies of blood vessels. There are two main issues, however, with this model: 1) the curve fits of experimental data are not always satisfactory, and 2) the material parameters may be oversensitive. A new type of strain measure in a generalized Hooke's law for blood vessels was recently proposed by our group to address these issues. The new model has one nonlinear parameter and six linear parameters. In this study, the stress-strain equation is validated by fitting the model to experimental data of porcine coronary arteries. Material constants of left anterior descending artery and right coronary artery for the Hooke's law were computed with a separable nonlinear least-squares method with an excellent goodness of fit. A parameter sensitivity analysis shows that the stability of material constants is improved compared with the exponential model and a biphasic model. A boundary value problem was solved to demonstrate that the model prediction can match the measured arterial deformation under experimental loading conditions. The validated constitutive relation will serve as a basis for the solution of various boundary value problems of cardiovascular biomechanics.

Association Fields via Cuspless Sub-Riemannian Geodesics in SE(2).

PubMed

Duits, R; Boscain, U; Rossi, F; Sachkov, Y

To model association fields that underly perceptional organization (gestalt) in psychophysics we consider the problem P curve of minimizing [Formula: see text] for a planar curve having fixed initial and final positions and directions. Here κ ( s ) is the curvature of the curve with free total length ℓ . This problem comes from a model of geometry of vision due to Petitot (in J. Physiol. Paris 97:265-309, 2003; Math. Inf. Sci. Humaines 145:5-101, 1999), and Citti & Sarti (in J. Math. Imaging Vis. 24(3):307-326, 2006). In previous work we proved that the range [Formula: see text] of the exponential map of the underlying geometric problem formulated on SE(2) consists of precisely those end-conditions ( x fin , y fin , θ fin ) that can be connected by a globally minimizing geodesic starting at the origin ( x in , y in , θ in )=(0,0,0). From the applied imaging point of view it is relevant to analyze the sub-Riemannian geodesics and [Formula: see text] in detail. In this article we show that [Formula: see text] is contained in half space x ≥0 and (0, y fin )≠(0,0) is reached with angle π ,show that the boundary [Formula: see text] consists of endpoints of minimizers either starting or ending in a cusp,analyze and plot the cones of reachable angles θ fin per spatial endpoint ( x fin , y fin ),relate the endings of association fields to [Formula: see text] and compute the length towards a cusp,analyze the exponential map both with the common arc-length parametrization t in the sub-Riemannian manifold [Formula: see text] and with spatial arc-length parametrization s in the plane [Formula: see text]. Surprisingly, s -parametrization simplifies the exponential map, the curvature formulas, the cusp-surface, and the boundary value problem,present a novel efficient algorithm solving the boundary value problem,show that sub-Riemannian geodesics solve Petitot's circle bundle model (cf. Petitot in J. Physiol. Paris 97:265-309, [2003]),show a clear similarity with association field lines and sub-Riemannian geodesics.

Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics

NASA Astrophysics Data System (ADS)

Rangan, Aaditya V.; Cai, David; Tao, Louis

2007-02-01

Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear boundary conditions. The PDEs themselves are self-consistently specified by parameters which are functions of the boundary values of the solution. The moment equations can be stiff in space and time. Numerical methods are presented here for efficiently and accurately solving these moment equations. The essential ingredients in our numerical methods include: (i) the system is discretized in time with an implicit Euler method within a spectral deferred correction framework, therefore, the PDEs of the kinetic theory are reduced to a sequence, in time, of boundary value problems (BVPs) with nonlinear boundary conditions; (ii) a set of auxiliary parameters is introduced to recast the original BVP with nonlinear boundary conditions as BVPs with linear boundary conditions - with additional algebraic constraints on the auxiliary parameters; (iii) a careful combination of two Newton's iterates for the nonlinear BVP with linear boundary condition, interlaced with a Newton's iterate for solving the associated algebraic constraints is constructed to achieve quadratic convergence for obtaining the solutions with self-consistent parameters. It is shown that a simple fixed-point iteration can only achieve a linear convergence for the self-consistent parameters. The practicability and efficiency of our numerical methods for solving the moment equations of the kinetic theory are illustrated with numerical examples. It is further demonstrated that the moment equations derived from the kinetic theory of neuronal network dynamics can very well capture the coarse-grained dynamical properties of integrate-and-fire neuronal networks.

Numerical simulation of Forchheimer flow to a partially penetrating well with a mixed-type boundary condition

NASA Astrophysics Data System (ADS)

Mathias, Simon A.; Wen, Zhang

2015-05-01

This article presents a numerical study to investigate the combined role of partial well penetration (PWP) and non-Darcy effects concerning the performance of groundwater production wells. A finite difference model is developed in MATLAB to solve the two-dimensional mixed-type boundary value problem associated with flow to a partially penetrating well within a cylindrical confined aquifer. Non-Darcy effects are incorporated using the Forchheimer equation. The model is verified by comparison to results from existing semi-analytical solutions concerning the same problem but assuming Darcy's law. A sensitivity analysis is presented to explore the problem of concern. For constant pressure production, Non-Darcy effects lead to a reduction in production rate, as compared to an equivalent problem solved using Darcy's law. For fully penetrating wells, this reduction in production rate becomes less significant with time. However, for partially penetrating wells, the reduction in production rate persists for much larger times. For constant production rate scenarios, the combined effect of PWP and non-Darcy flow takes the form of a constant additional drawdown term. An approximate solution for this loss term is obtained by performing linear regression on the modeling results.

Spatially averaged flow over a wavy boundary revisited

USGS Publications Warehouse

McLean, S.R.; Wolfe, S.R.; Nelson, J.M.

1999-01-01

Vertical profiles of streamwise velocity measured over bed forms are commonly used to deduce boundary shear stress for the purpose of estimating sediment transport. These profiles may be derived locally or from some sort of spatial average. Arguments for using the latter procedure are based on the assumption that spatial averaging of the momentum equation effectively removes local accelerations from the problem. Using analogies based on steady, uniform flows, it has been argued that the spatially averaged velocity profiles are approximately logarithmic and can be used to infer values of boundary shear stress. This technique of using logarithmic profiles is investigated using detailed laboratory measurements of flow structure and boundary shear stress over fixed two-dimensional bed forms. Spatial averages over the length of the bed form of mean velocity measurements at constant distances from the mean bed elevation yield vertical profiles that are highly logarithmic even though the effect of the bottom topography is observed throughout the water column. However, logarithmic fits of these averaged profiles do not yield accurate estimates of the measured total boundary shear stress. Copyright 1999 by the American Geophysical Union.

Low-Dispersion Scheme for Nonlinear Acoustic Waves in Nonuniform Flow

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Kaushik, Dinesh K.; Idres, Moumen

1997-01-01

The linear dispersion-relation-preserving scheme and its boundary conditions have been extended to the nonlinear Euler equations. This allowed computing, a nonuniform flowfield and a nonlinear acoustic wave propagation in such a medium, by the same scheme. By casting all the equations, boundary conditions, and the solution scheme in generalized curvilinear coordinates, the solutions were made possible for non-Cartesian domains and, for the better deployment of the grid points, nonuniform grid step sizes could be used. It has been tested for a number of simple initial-value and periodic-source problems. A simple demonstration of the difference between a linear and nonlinear propagation was conducted. The wall boundary condition, derived from the momentum equations and implemented through a pressure at a ghost point, and the radiation boundary condition, derived from the asymptotic solution to the Euler equations, have proven to be effective for the nonlinear equations and nonuniform flows. The nonreflective characteristic boundary conditions also have shown success but limited to the nonlinear waves in no mean flow, and failed for nonlinear waves in nonuniform flow.

A two-dimensional composite grid numerical model based on the reduced system for oceanography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xie, Y.F.; Browning, G.L.; Chesshire, G.

The proper mathematical limit of a hyperbolic system with multiple time scales, the reduced system, is a system that contains no high-frequency motions and is well posed if suitable boundary conditions are chosen for the initial-boundary value problem. The composite grid method, a robust and efficient grid-generation technique that smoothly and accurately treats general irregular boundaries, is used to approximate the two-dimensional version of the reduced system for oceanography on irregular ocean basins. A change-of-variable technique that substantially increases the accuracy of the model and a method for efficiently solving the elliptic equation for the geopotential are discussed. Numerical resultsmore » are presented for circular and kidney-shaped basins by using a set of analytic solutions constructed in this paper.« less

How an antenna launches its input power into radiation: thepattern of the Poynting vector at and near an antenna

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jackson, J.D.

2005-05-18

In this paper I first address the question of whether theseat of the power radiated by an antenna made of conducting members isdistributed over the "arms" of the antenna according tomore » $$ - \\bf J \\cdotE$$, where $$\\bf J$$ is the specified current density and $$\\bf E$$ is theelectric field produced by that source. Poynting's theorem permits only aglobal identification of the total input power, usually from a localizedgenerator, with the total power radiated to infinity, not a localcorrespondence of $$- \\bf J \\cdot E\\ d^3x $$ with some specific radiatedpower, $$r^2 \\bf S \\cdot \\hat r\\ d\\Omega $$. I then describe a modelantenna consisting of two perfectly conducting hemispheres of radius\\emph a separated by a small equatorial gap across which occurs thedriving oscillatory electric field. The fields and surface current aredetermined by solution of the boundary value problem. In contrast to thefirst approach (not a boundary value problem), the tangential electricfield vanishes on the metallic surface. There is no radial Poyntingvector at the surface. Numerical examples are shown to illustrate how theenergy flows from the input region of the gap and is guided near theantenna by its "arms" until it is launched at larger \\emph r/a into theradiation pattern determined by the value of \\emph ka.« less

An ignition-temperature model with two free interfaces in premixed flames

NASA Astrophysics Data System (ADS)

Brauner, Claude-Michel; Gordon, Peter V.; Zhang, Wen

2016-11-01

In this paper we consider an ignition-temperature zero-order reaction model of thermo-diffusive combustion. This model describes the dynamics of thick flames, which have recently received considerable attention in the physical and engineering literature. The model admits a unique (up to translations) planar travelling wave solution. This travelling wave solution is quite different from those usually studied in combustion theory. The main qualitative feature of this travelling wave is that it has two interfaces: the ignition interface where the ignition temperature is attained and the trailing interface where the concentration of deficient reactants reaches zero. We give a new mathematical framework for studying the cellular instability of such travelling front solutions. Our approach allows the analysis of a free boundary problem to be converted into the analysis of a boundary value problem having a fully nonlinear system of parabolic equations. The latter is very suitable for both mathematical and numerical analysis. We prove the existence of a critical Lewis number such that the travelling wave solution is stable for values of Lewis number below the critical one and is unstable for Lewis numbers that exceed this critical value. Finally, we discuss the results of numerical simulations of a fully nonlinear system that describes the perturbation dynamics of planar fronts. These simulations reveal, in particular, some very interesting 'two-cell' steady patterns of curved combustion fronts.

A model for the estimation of the surface fluxes of momentum, heat and moisture of the cloud topped marine atmospheric boundary layer from satellite measurable parameters. M.S. Thesis

NASA Technical Reports Server (NTRS)

Allison, D. E.

1984-01-01

A model is developed for the estimation of the surface fluxes of momentum, heat, and moisture of the cloud topped marine atmospheric boundary layer by use of satellite remotely sensed parameters. The parameters chosen for the problem are the integrated liquid water content, q sub li, the integrated water vapor content, q sub vi, the cloud top temperature, and either a measure of the 10 meter neutral wind speed or the friction velocity at the surface. Under the assumption of a horizontally homogeneous, well-mixed boundary layer, the model calculates the equivalent potential temperature and total water profiles of the boundary layer along with the boundary layer height from inputs of q sub li, q sub vi, and cloud top temperature. These values, along with the 10m neutral wind speed or friction velocity and the sea surface temperature are then used to estimate the surface fluxes. The development of a scheme to parameterize the integrated water vapor outside of the boundary layer for the cases of cold air outbreak and California coastal stratus is presented.

What do we actually mean by 'sociotechnical'? On values, boundaries and the problems of language.

PubMed

Klein, Lisl

2014-03-01

The term 'sociotechnical' was first coined in the context of industrial democracy. In comparing two projects on shipping in Esso to help define the concept, the essential categories were found to be where systems boundaries were set, and what factors were considered to be relevant 'human' characteristics. This is often discussed in terms of values. During the nineteen-sixties and seventies sociotechnical theory related to the shop-floor work system, and contingency theory to the organisation as a whole, the two levels being distinct. With the coming of information technology, this distinction became blurred; the term 'socio-structural' is proposed to describe the whole system. IT sometimes is the operating technology, it sometimes supports the operating technology, or it may sometimes be mistaken for the operating technology. This is discussed with reference to recent air accidents. Copyright © 2013 Elsevier Ltd and The Ergonomics Society. All rights reserved.