A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory
NASA Astrophysics Data System (ADS)
Stolk, Christiaan C.
2016-06-01
We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a discrete operator to be applied to the source and the wavefields are constructed. Their coefficients are piecewise polynomial functions of hk, chosen such that phase and amplitude errors are minimal. The phase errors of the scheme are very small, approximately as small as those of the 2-D quasi-stabilized FEM method and substantially smaller than those of alternatives in 3-D, assuming the same number of gridpoints per wavelength is used. In numerical experiments, accurate solutions are obtained in constant and smoothly varying media using meshes with only five to six points per wavelength and wave propagation over hundreds of wavelengths. When used as a coarse level discretization in a multigrid method the scheme can even be used with down to three points per wavelength. Tests on 3-D examples with up to 108 degrees of freedom show that with a recently developed hybrid solver, the use of coarser meshes can lead to corresponding savings in computation time, resulting in good simulation times compared to the literature.
A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation
Riyanti, C.D. . E-mail: C.D.Riyanti@tudelft.nl; Kononov, A.; Erlangga, Y.A.; Vuik, C.; Oosterlee, C.W.; Plessix, R.-E.; Mulder, W.A.
2007-05-20
We investigate the parallel performance of an iterative solver for 3D heterogeneous Helmholtz problems related to applications in seismic wave propagation. For large 3D problems, the computation is no longer feasible on a single processor, and the memory requirements increase rapidly. Therefore, parallelization of the solver is needed. We employ a complex shifted-Laplace preconditioner combined with the Bi-CGSTAB iterative method and use a multigrid method to approximate the inverse of the resulting preconditioning operator. A 3D multigrid method with 2D semi-coarsening is employed. We show numerical results for large problems arising in geophysical applications.
Absence of Critical Points of Solutions to the Helmholtz Equation in 3D
NASA Astrophysics Data System (ADS)
Alberti, Giovanni S.
2016-05-01
The focus of this paper is to show the absence of critical points for the solutions to the Helmholtz equation in a bounded domain {Ωsubset{R}3} , given by div(a nabla u_{ω}g)-ω qu_{ω}g=0&quad {in Ω,} u_{ω}g=g&quad{on partialΩ.} We prove that for an admissible g there exists a finite set of frequencies K in a given interval and an open cover {overline{Ω}=\\cup_{ωin K} Ω_{ω}} such that {|nabla u_{ω}g(x)| > 0} for every {ωin K} and {xinΩ_{ω}} . The set K is explicitly constructed. If the spectrum of this problem is simple, which is true for a generic domain {Ω} , the admissibility condition on g is a generic property.
Shim3d Helmholtz Solution Package
Energy Science and Technology Software Center (ESTSC)
2009-01-29
This suite of codes solves the Helmholtz Equation for the steady-state propagation of single-frequency electromagnetic radiation in an arbitrary 2D or 3D dielectric medium. Materials can be either transparent or absorptive (including metals) and are described entirely by their shape and complex dielectric constant. Dielectric boundaries are assumed to always fall on grid boundaries and the material within a single grid cell is considered to be uniform. Input to the problem is in the formmore » of a Dirichlet boundary condition on a single boundary, and may be either analytic (Gaussian) in shape, or a mode shape computed using a separate code (such as the included eigenmode solver vwave20), and written to a file. Solution is via the finite difference method using Jacobi iteration for 3D problems or direct matrix inversion for 2D problems. Note that 3D problems that include metals will require different iteration parameters than described in the above reference. For structures with curved boundaries not easily modeled on a rectangular grid, the auxillary codes helmholtz11(2D), helm3d (semivectoral), and helmv3d (full vectoral) are provided. For these codes the finite difference equations are specified on a topological regular triangular grid and solved using Jacobi iteration or direct matrix inversion as before. An automatic grid generator is supplied.« less
The point-source method for 3D reconstructions for the Helmholtz and Maxwell equations
NASA Astrophysics Data System (ADS)
Ben Hassen, M. F.; Erhard, K.; Potthast, R.
2006-02-01
We use the point-source method (PSM) to reconstruct a scattered field from its associated far field pattern. The reconstruction scheme is described and numerical results are presented for three-dimensional acoustic and electromagnetic scattering problems. We give new proofs of the algorithms, based on the Green and Stratton-Chu formulae, which are more general than with the former use of the reciprocity relation. This allows us to handle the case of limited aperture data and arbitrary incident fields. Both for 3D acoustics and electromagnetics, numerical reconstructions of the field for different settings and with noisy data are shown. For shape reconstruction in acoustics, we develop an appropriate strategy to identify areas with good reconstruction quality and combine different such regions into one joint function. Then, we show how shapes of unknown sound-soft scatterers are found as level curves of the total reconstructed field.
Preconditioning the Helmholtz Equation for Rigid Ducts
NASA Technical Reports Server (NTRS)
Baumeister, Kenneth J.; Kreider, Kevin L.
1998-01-01
An innovative hyperbolic preconditioning technique is developed for the numerical solution of the Helmholtz equation which governs acoustic propagation in ducts. Two pseudo-time parameters are used to produce an explicit iterative finite difference scheme. This scheme eliminates the large matrix storage requirements normally associated with numerical solutions to the Helmholtz equation. The solution procedure is very fast when compared to other transient and steady methods. Optimization and an error analysis of the preconditioning factors are present. For validation, the method is applied to sound propagation in a 2D semi-infinite hard wall duct.
Monopoles, instantons, and the Helmholtz equation
NASA Astrophysics Data System (ADS)
Franchetti, Guido; Maldonado, Rafael
2016-07-01
In this work we study the dimensional reduction of smooth circle invariant Yang-Mills instantons defined on 4-manifolds which asymptotically become circle fibrations over hyperbolic 3-space. A suitable choice of the 4-manifold metric within a specific conformal class gives rise to singular and smooth hyperbolic monopoles. A large class of monopoles is obtained if the conformal factor satisfies the Helmholtz equation on hyperbolic 3-space. We describe simple configurations and relate our results to the Jackiw-Nohl-Rebbi construction, for which we provide a geometric interpretation.
NASA Astrophysics Data System (ADS)
Wang, S.; De Hoop, M. V.; Xia, J.; Li, X.
2011-12-01
We consider the modeling of elastic seismic wave propagation on a rectangular domain via the discretization and solution of the inhomogeneous coupled Helmholtz equation in 3D, by exploiting a parallel multifrontal sparse direct solver equipped with Hierarchically Semi-Separable (HSS) structure to reduce the computational complexity and storage. In particular, we are concerned with solving this equation on a large domain, for a large number of different forcing terms in the context of seismic problems in general, and modeling in particular. We resort to a parsimonious mixed grid finite differences scheme for discretizing the Helmholtz operator and Perfect Matched Layer boundaries, resulting in a non-Hermitian matrix. We make use of a nested dissection based domain decomposition, and introduce an approximate direct solver by developing a parallel HSS matrix compression, factorization, and solution approach. We cast our massive parallelization in the framework of the multifrontal method. The assembly tree is partitioned into local trees and a global tree. The local trees are eliminated independently in each processor, while the global tree is eliminated through massive communication. The solver for the inhomogeneous equation is a parallel hybrid between multifrontal and HSS structure. The computational complexity associated with the factorization is almost linear with the size of the Helmholtz matrix. Our numerical approach can be compared with the spectral element method in 3D seismic applications.
Iterative solution of the Helmholtz equation
Larsson, E.; Otto, K.
1996-12-31
We have shown that the numerical solution of the two-dimensional Helmholtz equation can be obtained in a very efficient way by using a preconditioned iterative method. We discretize the equation with second-order accurate finite difference operators and take special care to obtain non-reflecting boundary conditions. We solve the large, sparse system of equations that arises with the preconditioned restarted GMRES iteration. The preconditioner is of {open_quotes}fast Poisson type{close_quotes}, and is derived as a direct solver for a modified PDE problem.The arithmetic complexity for the preconditioner is O(n log{sub 2} n), where n is the number of grid points. As a test problem we use the propagation of sound waves in water in a duct with curved bottom. Numerical experiments show that the preconditioned iterative method is very efficient for this type of problem. The convergence rate does not decrease dramatically when the frequency increases. Compared to banded Gaussian elimination, which is a standard solution method for this type of problems, the iterative method shows significant gain in both storage requirement and arithmetic complexity. Furthermore, the relative gain increases when the frequency increases.
Multigrid and cyclic reduction applied to the Helmholtz equation
NASA Technical Reports Server (NTRS)
Brackenridge, Kenneth
1993-01-01
We consider the Helmholtz equation with a discontinuous complex parameter and inhomogeneous Dirichlet boundary conditions in a rectangular domain. A variant of the direct method of cyclic reduction (CR) is employed to facilitate the design of improved multigrid (MG) components, resulting in the method of CR-MG. We demonstrate the improved convergence properties of this method.
Kelvin-Helmholtz instability in a current-vortex sheet at a 3D magnetic null
Wyper, P. F.; Pontin, D. I.
2013-03-15
We report here, for the first time, an observed instability of a Kelvin-Helmholtz nature occurring in a fully three-dimensional (3D) current-vortex sheet at the fan plane of a 3D magnetic null point. The current-vortex layer forms self-consistently in response to foot point driving around the spine lines of the null. The layer first becomes unstable at an intermediate distance from the null point, with the instability being characterized by a rippling of the fan surface and a filamentation of the current density and vorticity in the shear layer. Owing to the 3D geometry of the shear layer, a branching of the current filaments and vortices is observed. The instability results in a mixing of plasma between the two topologically distinct regions of magnetic flux on either side of the fan separatrix surface, as flux is reconnected across this surface. We make a preliminary investigation of the scaling of the system with the dissipation parameters. Our results indicate that the fan plane separatrix surface is an ideal candidate for the formation of current-vortex sheets in complex magnetic fields and, therefore, the enhanced heating and connectivity change associated with the instabilities of such layers.
Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C
2011-06-01
The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well. PMID:21643384
Volume integrals of ellipsoids associated with the inhomogeneous Helmholtz equation
NASA Technical Reports Server (NTRS)
Fu, L. S.; Mura, T.
1982-01-01
Problems of wave phenomena in the fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the inhomogeneous Helmholtz equation, for an ellipsoidal region. By using appropriate Taylor series expansions and the multinomial theorem, these volume integrals are obtained in series form for regions r greater than r-prime and r less than r-prime, where r and r-prime are the distances from the origin to the point of observation and the source. Derivatives of these integrals are easily evaluated. When the wavenumber approaches zero the results reduce directly to the potentials of ellipsoids of variable densities.
Precise evaluation of the Helmholtz equation for optical propagation.
Pond, John E; Sutton, George W
2015-01-01
A precise computational integration of the Helmholtz equation was performed for laser propagation of an electromagnetic wave with no approximations or linearization. This computation integration was performed using 64-bit processors. This is illustrated for a uniform monochromatic beam from a circular aperture that has a uniform intensity. It predicts many Arago spots and near-field intensity fluctuations for a large ratio of aperture size to wavelength and converges to the usual Airy pattern in the far field. PMID:25531618
On the vector Helmholtz equation in toroidal waveguides
Biro, Thomas
2005-02-15
A wave splitting method is proposed to solve the problem of propagation of microwaves in a circular waveguide bend of circular cross section. The splitting method, applied to the vector Helmholtz equation, gives a stable solution in terms of waves propagating to the right and to the left in the bend. The formulation is particularly transparent for analyzing the scattering properties of toroidal bends. The basis for the transparency of the method is that the wave splitting is formally exact as the exponential of the square root of a differential operator. The modal functions of the straight cylindrical waveguide are chosen as basis functions in the transverse quasi-toroidal variables.
A double-sweeping preconditioner for the Helmholtz equation
NASA Astrophysics Data System (ADS)
Eslaminia, Mehran; Guddati, Murthy N.
2016-06-01
A new preconditioner is developed to increase the efficiency of iterative solution of the Helmholtz equation. The key idea of the proposed preconditioner is to split the domain of interest into smaller subdomains and sequentially approximate the forward and backward components of the solution. The sequential solution is facilitated by approximate interface conditions that ignore the effect of multiple reflections. The efficiency of the proposed method is tested using various 2-D heterogeneous media. We observe that the proposed preconditioner results in good convergence, with number of iterations growing very slowly with increasing frequency. We also note that the mesh size and number of subdomains do not affect the convergence rate. Finally, we find that the overall computational time is much smaller than that of the sweeping preconditioner.
Reck, Kasper; Thomsen, Erik V; Hansen, Ole
2011-01-31
The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution. PMID:21368995
Diffractive 3D XUV optics at Helmholtz-Zentrum Berlin, recent developments
NASA Astrophysics Data System (ADS)
Brzhezinskaya, Maria; Firsov, Alexander; Erko, Alexei
2014-09-01
The 2-Dimensional and 3-Dimensional variable line spacing (VLS) gratings based on total external reflection give the unique possibility for spectroscopy and focusing in application to 4th and 5th generation synchrotron sources. We focus on the elaboration of novel approaches for design and fabrication of 3D VLS working in the entire energy range, from THz to hard X-rays. These optical elements have unique combination of properties and can operate at all XUV sources including Free Electron Lasers (FELs), Energy Recovery Linacs (ERLs) and High Harmonic Generators (HHGs). Such 3D DOEs are able to cover the energy range of up to 20 keV with energy resolution λ/Δλ ≥ 1000 for soft x-ray and λ/Δλ ≥ 10000 for hard x-ray. We fabricate 3D VLS for time-resolved spectroscopy (energy range 100 - 2000 eV, 7500-9500 eV), FELs and ERLs (energy range up to 3 keV), and HHGs (energy range 10 - 200 eV).
Numerical solution of the nonlinear Helmholtz equation using nonorthogonal expansions
Fibich, G. . E-mail: fibich@math.tau.ac.il; Tsynkov, S. . E-mail: tsynkov@math.ncsu.edu
2005-11-20
In [J. Comput. Phys. 171 (2001) 632-677] we developed a fourth-order numerical method for solving the nonlinear Helmholtz equation which governs the propagation of time-harmonic laser beams in media with a Kerr-type nonlinearity. A key element of the algorithm was a new nonlocal two-way artificial boundary condition (ABC), set in the direction of beam propagation. This two-way ABC provided for reflectionless propagation of the outgoing waves while also fully transmitting the given incoming beam at the boundaries of the computational domain. Altogether, the algorithm of [J. Comput. Phys. 171 (2001) 632-677] has allowed for a direct simulation of nonlinear self-focusing without neglecting nonparaxial effects and backscattering. To the best of our knowledge, this capacity has never been achieved previously in nonlinear optics. In the current paper, we propose an improved version of the algorithm. The principal innovation is that instead of using the Dirichlet boundary conditions in the direction orthogonal to that of the laser beam propagation, we now introduce Sommerfeld-type local radiation boundary conditions, which are constructed directly in the discrete framework. Numerically, implementation of the Sommerfeld conditions requires evaluation of eigenvalues and eigenvectors for a non-Hermitian matrix. Subsequently, the separation of variables, which is a key building block of the aforementioned nonlocal ABC, is implemented through an expansion with respect to the nonorthogonal basis of the eigenvectors. Numerical simulations show that the new algorithm offers a considerable improvement in its numerical performance, as well as in the range of physical phenomena that it is capable of simulating.
NASA Astrophysics Data System (ADS)
Luo, Songting; Qian, Jianliang; Burridge, Robert
2014-08-01
In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation so that the Helmholtz equation may be viewed as an evolution equation in one of the spatial directions. With such applications in mind, we propose a new Eulerian computational geometrical-optics method, dubbed the fast Huygens sweeping method, for computing Green functions of Helmholtz equations in inhomogeneous media in the high-frequency regime and in the presence of caustics. The first novelty of the new method is that the Huygens-Kirchhoff secondary source principle is used to integrate many locally valid asymptotic solutions to yield a globally valid asymptotic solution so that caustics associated with the usual geometrical-optics ansatz can be treated automatically. The second novelty is that a butterfly algorithm is adapted to carry out the matrix-vector products induced by the Huygens-Kirchhoff integration in O(Nlog N) operations, where N is the total number of mesh points, and the proportionality constant depends on the desired accuracy and is independent of the frequency parameter. To reduce the storage of the resulting traveltime and amplitude tables, we compress each table into a linear combination of tensor-product based multivariate Chebyshev polynomials so that the information of each table is encoded into a small number of Chebyshev coefficients. The new method enjoys the following desired features: (1) it precomputes a set of local traveltime and amplitude tables; (2) it automatically takes care of caustics; (3) it constructs Green functions of the Helmholtz equation for arbitrary frequencies and for many point sources; (4) for a specified number of points per wavelength it constructs each Green function in nearly optimal complexity in terms of the total number of mesh points, where the prefactor of the complexity only depends on the specified accuracy and is independent of the frequency parameter. Both two-dimensional (2-D) and three-dimensional (3
A spectral boundary integral equation method for the 2-D Helmholtz equation
NASA Technical Reports Server (NTRS)
Hu, Fang Q.
1994-01-01
In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.
SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.
Wan, Xiaohai; Li, Zhilin
2012-06-01
Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size. PMID:22701346
Derivation of new 3D discrete ordinate equations
Ahrens, C. D.
2012-07-01
The Sn equations have been the workhorse of deterministic radiation transport calculations for many years. Here we derive two new angular discretizations of the 3D transport equation. The first set of equations, derived using Lagrange interpolation and collocation, retains the classical Sn structure, with the main difference being how the scattering source is calculated. Because of the formal similarity with the classical S n equations, it should be possible to modify existing computer codes to take advantage of the new formulation. In addition, the new S n-like equations correctly capture delta function scattering. The second set of equations, derived using a Galerkin technique, does not retain the classical Sn structure because the streaming term is not diagonal. However, these equations can be cast into a form similar to existing methods developed to reduce ray effects. Numerical investigation of both sets of equations is under way. (authors)
Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.
Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y C
2015-01-01
A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals. PMID:26064591
A note on singularities of the 3-D Euler equation
NASA Technical Reports Server (NTRS)
Tanveer, S.
1994-01-01
In this paper, we consider analytic initial conditions with finite energy, whose complex spatial continuation is a superposition of a smooth background flow and a singular field. Through explicit calculation in the complex plane, we show that under some assumptions, the solution to the 3-D Euler equation ceases to be analytic in the real domain in finite time.
Li,Jing; Tu, Xuemin
2008-12-10
A variant of balancing domain decomposition method by constraints (BDDC) is proposed for solving a class of indefinite system of linear equations, which arises from the finite element discretization of the Helmholtz equation of time-harmonic wave propagation in a bounded interior domain. The proposed BDDC algorithm is closely related to the dual-primal finite element tearing and interconnecting algorithm for solving Helmholtz equations (FETI-DPH). Under the condition that the diameters of the subdomains are small enough, the rate of convergence is established which depends polylogarithmically on the dimension of the individual subdomain problems and which improves with the decrease of the subdomain diameters. These results are supported by numerical experiments of solving a Helmholtz equation on a two-dimensional square domain.
Active exterior cloaking for the 2D Laplace and Helmholtz equations.
Vasquez, Fernando Guevara; Milton, Graeme W; Onofrei, Daniel
2009-08-14
A new cloaking method is presented for 2D quasistatics and the 2D Helmholtz equation that we speculate extends to other linear wave equations. For 2D quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to finding a polynomial which is close to 1 in a disk and close to 0 in another disk, and such a polynomial is constructed. For the 2D Helmholtz equation it is numerically shown that three exterior cloaking devices placed around the object suffice to hide it. PMID:19792644
Finite-difference solutions of the 3-D eikonal equation
Fei, Tong; Fehler, M.C.; Hildebrand, S.T.
1995-12-31
Prestack Kirchhoff depth migration requires the computation of traveltimes from surface source and receiver locations to subsurface image locations. In 3-D problems, computational efficiency becomes important. Finite-difference solutions of the eikonal equation provide computationally efficient methods for generating the traveltime information. Here, a novel finite-difference solutions of the eikonal equation provide computationally efficient methods for generating the traveltime information. Here, a novel finite-difference method for computing the first arrival traveltime by solving the eikonal equation has been developed in Cartesian coordinates. The method, which is unconditionally stable and computationally efficient, can handle instabilities due to caustics and provide information about head waves. The comparison of finite-difference solutions of the acoustic wave equation with the traveltime solutions from the eikonal equation in various structure models demonstrate that the method developed here can provide correct first arrival traveltime information even in areas of complex velocity structure.
A parallel algorithm for solving the 3d Schroedinger equation
Strickland, Michael; Yager-Elorriaga, David
2010-08-20
We describe a parallel algorithm for solving the time-independent 3d Schroedinger equation using the finite difference time domain (FDTD) method. We introduce an optimized parallelization scheme that reduces communication overhead between computational nodes. We demonstrate that the compute time, t, scales inversely with the number of computational nodes as t {proportional_to} (N{sub nodes}){sup -0.95} {sup {+-} 0.04}. This makes it possible to solve the 3d Schroedinger equation on extremely large spatial lattices using a small computing cluster. In addition, we present a new method for precisely determining the energy eigenvalues and wavefunctions of quantum states based on a symmetry constraint on the FDTD initial condition. Finally, we discuss the usage of multi-resolution techniques in order to speed up convergence on extremely large lattices.
NASA Astrophysics Data System (ADS)
Khalilov, E. H.
2016-07-01
The surface integral equation for a spatial mixed boundary value problem for the Helmholtz equation is considered. At a set of chosen points, the equation is replaced with a system of algebraic equations, and the existence and uniqueness of the solution of this system is established. The convergence of the solutions of this system to the exact solution of the integral equation is proven, and the convergence rate of the method is determined.
Numerical simulation of vortex breakdown via 3-D Euler equations
NASA Astrophysics Data System (ADS)
Le, T. H.; Mege, P.; Morchoisne, Y.
1990-06-01
The long term goal is the modeling of vortex breakdown that occurs in some aerodynamic configurations at high angle of attack, (i.e., fighters with highly swept delta wings or missiles). A numerical simulation was made based on solving the 3-D Euler equations for an usteady incompressible flow. Preliminary results were obtained using a pressure-velocity formulation with periodic boundary conditions, the Euler equations being discretized by 2nd order finite difference schemes. The continuation to this work by implementing more realistic boundary conditions and 4th order finite difference discretization schemes are presented.
Two-equation turbulence modeling for 3-D hypersonic flows
NASA Technical Reports Server (NTRS)
Bardina, J. E.; Coakley, T. J.; Marvin, J. G.
1992-01-01
An investigation to verify, incorporate and develop two-equation turbulence models for three-dimensional high speed flows is presented. The current design effort of hypersonic vehicles has led to an intensive study of turbulence models for compressible hypersonic flows. This research complements an extensive review of experimental data and the current development of 2D turbulence models. The review of experimental data on 2D and 3D flows includes complex hypersonic flows with pressure profiles, skin friction, wall heat transfer, and turbulence statistics data. In a parallel effort, turbulence models for high speed flows have been tested against flat plate boundary layers, and are being tested against the 2D database. In the present paper, we present the results of 3D Navier-Stokes numerical simulations with an improved k-omega two-equation turbulence model against experimental data and empirical correlations of an adiabatic flat plate boundary layer, a cold wall flat plate boundary layer, and a 3D database flow, the interaction of an oblique shock wave and a thick turbulent boundary layer with a free stream Mach number = 8.18 and Reynolds number = 5 x 10 to the 6th.
Volume integrals associated with the inhomogeneous Helmholtz equation. Part 1: Ellipsoidal region
NASA Technical Reports Server (NTRS)
Fu, L. S.; Mura, T.
1983-01-01
Problems of wave phenomena in fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) to alpha(2), for the case of an ellipsoidal region. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r 4' and r r', where r and r' are distances from the origin to the point of observation and source, respectively. Derivatives of these integrals are easily evaluated. When the wave number approaches zero, the results reduce directly to the potentials of variable densities.
Potentially singular solutions of the 3D axisymmetric Euler equations
Luo, Guo; Hou, Thomas Y.
2014-01-01
The question of finite-time blowup of the 3D incompressible Euler equations is numerically investigated in a periodic cylinder with solid boundaries. Using rotational symmetry, the equations are discretized in the (2D) meridian plane on an adaptive (moving) mesh and is integrated in time with adaptively chosen time steps. The vorticity is observed to develop a ring-singularity on the solid boundary with a growth proportional to ∼(ts − t)−2.46, where ts ∼ 0.0035056 is the estimated singularity time. A local analysis also suggests the existence of a self-similar blowup. The simulations stop at τ2 = 0.003505 at which time the vorticity amplifies by more than (3 × 108)-fold and the maximum mesh resolution exceeds (3 × 1012)2. The vorticity vector is observed to maintain four significant digits throughout the computations. PMID:25157172
Modeling tree crown dynamics with 3D partial differential equations.
Beyer, Robert; Letort, Véronique; Cournède, Paul-Henry
2014-01-01
We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications. PMID:25101095
On the solution of the Helmholtz equation on regions with corners.
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. PMID:27482110
Equations on knot polynomials and 3d/5d duality
Mironov, A.; Morozov, A.
2012-09-24
We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include linear skein relations, quadratic Plucker relations, as well as 'differential' and (quantum) A-polynomial structures. We pay a special attention to identity between the A-polynomial equations for knots and Baxter equations for quantum relativistic integrable systems, related through Seiberg-Witten theory to 5d super-Yang-Mills models and through the AGT relation to the q-Virasoro algebra. This identity is an important ingredient of emerging a 3d- 5d generalization of the AGT relation. The shape of the Baxter equation (including the values of coefficients) depend on the choice of the knot/braid. Thus, like the case of KP integrability, where (some, so far torus) knots parameterize particular points of the Universal Grassmannian, in this relation they parameterize particular points in the moduli space of many-body integrable systems of relativistic type.
A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions
NASA Technical Reports Server (NTRS)
Sun, Xian-He; Zhuang, Yu
1997-01-01
In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.
Chang, Zheng; Zhou, Xiaoming; Hu, Jin; Hu, Gengkai
2010-02-15
In a recent paper, Chen et al. [Opt. Express 17, 3581 (2009)] develop an approach to design invisible cloaks with controllable constitutive parameters by adjusting the constant k in the Helmholtz's equation. In this comment, we discuss the limitation of the free parameter k in designing cloaks. It is found that the real constant k can be chosen only as limited values in order to avoid the singular material parameters. PMID:20389403
Fathi, S. M. Saberi
2010-12-15
In this paper we first show in the framework of quaternion analysis how the fundamental solutions of the Dirac operators with vector potential can be obtained. Then, we use the obtained results to present a derivation of the exact analytic Green function for the Helmholtz equation, i.e., ({Delta}+|a(x)|{sup 2})G{sub 0}(x)={delta}(x), for the case a(x) is a monogenic (analytic) vector potential.
Chen, Xi; Fu, Yunqi; Yuan, Naichang
2009-03-01
An approach to design an invisible cloak with controlled constitutive parameters and arbitrary shaped boundaries is presented. Helmholtz's equation is adopted to establish a mapping between original and transformed coordinates inside the cloak. Then the constitutive parameters are obtained by the established mapping. The analytical solution of a regular cloak and the numerical solution of an irregular cloak both verify that that our method will guide electromagnetic wave efficiently and control the constitutive parameters of the cloak conveniently. It has great significance in realizing a cloak practically. PMID:19259197
Petrov-Galerkin's method hybrid with finite element into the Helmholtz equation solution. Part II
NASA Astrophysics Data System (ADS)
Rabadan Malda, Itzala; Salazar Cordero, Emigdio; Ortega Herrera, Jose Angel
2002-11-01
This work proposes a hybridization between Petrov-Galerkins numeric method and finite element method (FEM) to resolve Helmholtz equation when dominion is an open or semiopen tube-shaped configuration and with determinate number of holes over cylindrical surface. It's pretended to solve these kind of cavities, thereby it allows us to obtain very important design parameters like: cavity length, quantity, size and distance between toneholes, form and size of mouthpiece or outlet. These parameters are design basis into acoustic and musical instrumentation: baffles outlet pipes, diffusers, silencers, flutes, oboes, saxophones, trumpets, quenas, and many more. In this way it's expected to determine advantages of this numeric method above another using actually.
Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions
NASA Technical Reports Server (NTRS)
Hodge, Steve L.; Zorumski, William E.; Watson, Willie R.
1995-01-01
The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.
Vortex lattices generated by the Kelvin-Helmholtz instability in the Gross-Pitaevskii equation
Ohta, A.; Kashiwa, R.; Sakaguchi, H.
2010-11-15
Vortex streets are formed from sheared initial conditions in classical fluids even without viscosity, which is called the Kelvin-Helmholtz instability. We demonstrate that similar vortex streets are generated from sheared initial conditions by the direct numerical simulation of the Gross-Pitaevskii (GP) equation which describes the dynamics of the Bose-Einstein condensates. Furthermore, we show the vortex-lattice formation from sheared initial conditions analogous to the rigid-body rotation in the GP equation under a rotating harmonic potential. The vortex-lattice formation by the dynamical instability in the system without energy dissipation differs from the vortex-lattice formation process by the imaginary time evolution of the GP equation where the lowest energy state is obtained.
A general approach for high order absorbing boundary conditions for the Helmholtz equation
NASA Astrophysics Data System (ADS)
Zarmi, Asaf; Turkel, Eli
2013-06-01
When solving a scattering problem in an unbounded space, one needs to implement the Sommerfeld condition as a boundary condition at infinity, to ensure no energy penetrates the system. In practice, solving a scattering problem involves truncating the region and implementing a boundary condition on an artificial outer boundary. Bayliss, Gunzburger and Turkel (BGT) suggested an Absorbing Boundary Condition (ABC) as a sequence of operators aimed at annihilating elements from the solution's series representation. Their method was practical only up to a second order condition. Later, Hagstrom and Hariharan (HH) suggested a method which used auxiliary functions and enabled implementation of higher order conditions. We compare various absorbing boundary conditions (ABCs) and introduce a new method to construct high order ABCs, generalizing the HH method. We then derive from this general method ABCs based on different series representations of the solution to the Helmholtz equation - in polar, elliptical and spherical coordinates. Some of these ABCs are generalizations of previously constructed ABCs and some are new. These new ABCs produce accurate solutions to the Helmholtz equation, which are much less dependent on the various parameters of the problem, such as the value of k, or the eccentricity of the ellipse. In addition to constructing new ABCs, our general method sheds light on the connection between various ABCs. Computations are presented to verify the high accuracy of these new ABCs.
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. PMID:19173406
High-order numerical solution of the nonlinear Helmholtz equation with axial symmetry
NASA Astrophysics Data System (ADS)
Baruch, G.; Fibich, G.; Tsynkov, S.
2007-07-01
The nonlinear Helmholtz (NLH) equation models the propagation of intense laser beams in a Kerr medium. The NLH takes into account the effects of nonparaxiality and backward scattering that are neglected in the more common nonlinear Schrodinger model. In [G. Fibich, S. Tsynkov, High-order two-way artificial boundary conditions for nonlinear wave propagation with backscattering, J. Comput. Phys., 171 (2001) 632-677] and [G. Fibich, S. Tsynkov, Numerical solution of the nonlinear Helmholtz equation using nonorthogonal expansions, J. Comput. Phys., 210 (2005) 183-224], a novel high-order numerical method for solving the NLH was introduced and implemented in the case of a two-dimensional Cartesian geometry. The NLH was solved iteratively, using the separation of variables and a special nonlocal two-way artificial boundary condition applied to the resulting decoupled linear systems. In the current paper, we propose a major improvement to the previous method. Instead of using LU decomposition after the separation of variables, we employ an efficient summation rule that evaluates convolution with the discrete Green's function. We also extend the method to a three-dimensional setting with cylindrical symmetry, under both Dirichlet and Sommerfeld-type transverse boundary conditions.
Compressed Liquid Densities and Helmholtz Energy Equation of State for Fluoroethane (R161)
NASA Astrophysics Data System (ADS)
Qi, Haiyan; Fang, Dan; Gao, Kehui; Meng, Xianyang; Wu, Jiangtao
2016-06-01
In this study, compressed liquid densities of Fluoroethane (R161, CAS No. 353-36-6) were measured using a high-pressure vibrating-tube densimeter over the temperature range from (283 to 363) K with pressures up to 100 MPa. A Helmholtz energy equation of state for R161 was developed from these density measurements and other experimental thermodynamic property data from the literature. The formulation is valid for temperatures from the triple point temperature of 130 K to 420 K with pressures up to 100 MPa. The approximate uncertainties of properties calculated with the new equation of state are estimated to be 0.25 % in density, 0.2 % in saturated liquid density between 230 K and 320 K, and 0.2 % in vapor pressure below 350 K. Deviations in the critical region are higher for all properties. The extrapolation behavior of the new formulation at high temperatures and high pressures is reasonable.
Exponential Mixing of the 3D Stochastic Navier-Stokes Equations Driven by Mildly Degenerate Noises
Albeverio, Sergio; Debussche, Arnaud; Xu Lihu
2012-10-15
We prove the strong Feller property and exponential mixing for 3D stochastic Navier-Stokes equation driven by mildly degenerate noises (i.e. all but finitely many Fourier modes being forced) via a Kolmogorov equation approach.
NASA Astrophysics Data System (ADS)
Lu, Wangtao; Qian, Jianliang; Burridge, Robert
2016-05-01
In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation so that the Helmholtz equation can be viewed as an evolution equation in one of the spatial directions. With such applications in mind, starting from Babich's expansion, we develop a new high-order asymptotic method, which we dub the fast Huygens sweeping method, for solving point-source Helmholtz equations in inhomogeneous media in the high-frequency regime and in the presence of caustics. The first novelty of this method is that we develop a new Eulerian approach to compute the asymptotics, i.e. the traveltime function and amplitude coefficients that arise in Babich's expansion, yielding a locally valid solution, which is accurate close enough to the source. The second novelty is that we utilize the Huygens-Kirchhoff integral to integrate many locally valid wavefields to construct globally valid wavefields. This automatically treats caustics and yields uniformly accurate solutions both near the source and remote from it. The third novelty is that the butterfly algorithm is adapted to accelerate the Huygens-Kirchhoff summation, achieving nearly optimal complexity O (Nlog N), where N is the number of mesh points; the complexity prefactor depends on the desired accuracy and is independent of the frequency. To reduce the storage of the resulting tables of asymptotics in Babich's expansion, we use the multivariable Chebyshev series expansion to compress each table by encoding the information into a small number of coefficients. The new method enjoys the following desired features. First, it precomputes the asymptotics in Babich's expansion, such as traveltime and amplitudes. Second, it takes care of caustics automatically. Third, it can compute the point-source Helmholtz solution for many different sources at many frequencies simultaneously. Fourth, for a specified number of points per wavelength, it can construct the wavefield in nearly optimal complexity in terms
NASA Technical Reports Server (NTRS)
Bayliss, A.; Goldstein, C. I.; Turkel, E.
1984-01-01
The Helmholtz Equation (-delta-K(2)n(2))u=0 with a variable index of refraction, n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. A numerical algorithm was developed and a computer code implemented that can effectively solve this equation in the intermediate frequency range. The equation is discretized using the finite element method, thus allowing for the modeling of complicated geometrices (including interfaces) and complicated boundary conditions. A global radiation boundary condition is imposed at the far field boundary that is exact for an arbitrary number of propagating modes. The resulting large, non-selfadjoint system of linear equations with indefinite symmetric part is solved using the preconditioned conjugate gradient method applied to the normal equations. A new preconditioner is developed based on the multigrid method. This preconditioner is vectorizable and is extremely effective over a wide range of frequencies provided the number of grid levels is reduced for large frequencies. A heuristic argument is given that indicates the superior convergence properties of this preconditioner.
On the Implementation of 3D Galerkin Boundary Integral Equations
Nintcheu Fata, Sylvain; Gray, Leonard J
2010-01-01
In this article, a reverse contribution technique is proposed to accelerate the construction of the dense influence matrices associated with a Galerkin approximation of singular and hypersingular boundary integral equations of mixed-type in potential theory. In addition, a general-purpose sparse preconditioner for boundary element methods has also been developed to successfully deal with ill-conditioned linear systems arising from the discretization of mixed boundary-value problems on non-smooth surfaces. The proposed preconditioner, which originates from the precorrected-FFT method, is sparse, easy to generate and apply in a Krylov subspace iterative solution of discretized boundary integral equations. Moreover, an approximate inverse of the preconditioner is implicitly built by employing an incomplete LU factorization. Numerical experiments involving mixed boundary-value problems for the Laplace equation are included to illustrate the performance and validity of the proposed techniques.
Effect of triangular element orientation on finite element solutions of the Helmholtz equation
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1986-01-01
The Galerkin finite element solutions for the scalar homogeneous Helmholtz equation are presented for no reflection, hard wall, and potential relief exit terminations with a variety of triangular element orientations. For this group of problems, the correlation between the accuracy of the solution and the orientation of the linear triangle is examined. Nonsymmetric element patterns are found to give generally poor results in the model problems investigated, particularly for cases where standing waves exist. For a fixed number of vertical elements, the results showed that symmetric element patterns give much better agreement with corresponding exact analytical results. In laminated wave guide application, the symmetric pyramid pattern is convenient to use and is shown to give excellent results.
Wave Gradiometry and Helmholtz Equation Solutions Applied to USArray across the Contiguous U.S.
NASA Astrophysics Data System (ADS)
Liu, Y.; Holt, W. E.
2015-12-01
Wave gradiometry is an array processing technique utilizing the shape of seismic wavefields captured by USArray TA stations to determine fundamental wave propagation characteristics. We first explore a compatibility relation that links spatial gradients of the wavefield with the displacements and the time derivatives of displacements through two unknown coefficients Aand B, which are solved through iterative, damped least-square inversion, to provide estimates of phase velocity, back-azimuth, radiation pattern and geometrical spreading. We show that the A-coefficient corresponds to the gradient of logarithmic amplitude and the B-coefficient corresponds approximately to the local dynamic phase velocity. These vector fields are interpolated to explore a second compatibility relation through solutions to the Helmholtz equation. For most wavefields passing through the eastern U.S., we show that the A-coefficients are generally orthogonal to the B-coefficients. Where they are not completely orthogonal, there is a strong positive correlation between the gradients of B-coefficients and changes in geometrical spreading, which can be further linked with areas of strong energy focusing and defocusing. We then obtain isotropic phase velocity maps across the contiguous United States for 20 - 150 s Rayleigh wave by stacking results from 700 earthquakes. The strong velocity variations in the western U.S. correlate well with known geological features and the am- plitude correction terms from Helmholtz equation solutions generally improve the resolution of small-scale structures for all periods analyzed. We also observe a velocity change along the approximate boundary of the early Paleozoic continental margin in the eastern U.S and two significant low velocity anomalies within the central Appalachians, one centered where Eocene basaltic volcanism has occurred, and the other within the northeastern U.S., possibly associated with the Great Meteor Hotspot track.
2D/1D approximations to the 3D neutron transport equation. I: Theory
Kelley, B. W.; Larsen, E. W.
2013-07-01
A new class of '2D/1D' approximations is proposed for the 3D linear Boltzmann equation. These approximate equations preserve the exact transport physics in the radial directions x and y and diffusion physics in the axial direction z. Thus, the 2D/1D equations are more accurate approximations of the 3D Boltzmann equation than the conventional 3D diffusion equation. The 2D/1D equations can be systematically discretized, to yield accurate simulation methods for 3D reactor core problems. The resulting solutions will be more accurate than 3D diffusion solutions, and less expensive to generate than standard 3D transport solutions. In this paper, we (i) show that the simplest 2D/1D equation has certain desirable properties, (ii) systematically discretize this equation, and (iii) derive a stable iteration scheme for solving the discrete system of equations. In a companion paper [1], we give numerical results that confirm the theoretical predictions of accuracy and iterative stability. (authors)
NASA Astrophysics Data System (ADS)
Nguyen, N. C.; Peraire, J.; Reitich, F.; Cockburn, B.
2015-06-01
We introduce a new hybridizable discontinuous Galerkin (HDG) method for the numerical solution of the Helmholtz equation over a wide range of wave frequencies. Our approach combines the HDG methodology with geometrical optics in a fashion that allows us to take advantage of the strengths of these two methodologies. The phase-based HDG method is devised as follows. First, we enrich the local approximation spaces with precomputed phases which are solutions of the eikonal equation in geometrical optics. Second, we propose a novel scheme that combines the HDG method with ray tracing to compute multivalued solution of the eikonal equation. Third, we utilize the proper orthogonal decomposition to remove redundant modes and obtain locally orthogonal basis functions which are then used to construct the global approximation spaces of the phase-based HDG method. And fourth, we propose an appropriate choice of the stabilization parameter to guarantee stability and accuracy for the proposed method. Numerical experiments presented show that optimal orders of convergence are achieved, that the number of degrees of freedom to achieve a given accuracy is independent of the wave number, and that the number of unknowns required to achieve a given accuracy with the proposed method is orders of magnitude smaller than that with the standard finite element method.
Helmholtz and parabolic equation solutions to a benchmark problem in ocean acoustics.
Larsson, Elisabeth; Abrahamsson, Leif
2003-05-01
The Helmholtz equation (HE) describes wave propagation in applications such as acoustics and electromagnetics. For realistic problems, solving the HE is often too expensive. Instead, approximations like the parabolic wave equation (PE) are used. For low-frequency shallow-water environments, one persistent problem is to assess the accuracy of the PE model. In this work, a recently developed HE solver that can handle a smoothly varying bathymetry, variable material properties, and layered materials, is used for an investigation of the errors in PE solutions. In the HE solver, a preconditioned Krylov subspace method is applied to the discretized equations. The preconditioner combines domain decomposition and fast transform techniques. A benchmark problem with upslope-downslope propagation over a penetrable lossy seamount is solved. The numerical experiments show that, for the same bathymetry, a soft and slow bottom gives very similar HE and PE solutions, whereas the PE model is far from accurate for a hard and fast bottom. A first attempt to estimate the error is made by computing the relative deviation from the energy balance for the PE solution. This measure gives an indication of the magnitude of the error, but cannot be used as a strict error bound. PMID:12765364
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Webb, Jay C.
1994-01-01
In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The
First-order system least-squares for the Helmholtz equation
Lee, B.; Manteuffel, T.; McCormick, S.; Ruge, J.
1996-12-31
We apply the FOSLS methodology to the exterior Helmholtz equation {Delta}p + k{sup 2}p = 0. Several least-squares functionals, some of which include both H{sup -1}({Omega}) and L{sup 2}({Omega}) terms, are examined. We show that in a special subspace of [H(div; {Omega}) {intersection} H(curl; {Omega})] x H{sup 1}({Omega}), each of these functionals are equivalent independent of k to a scaled H{sup 1}({Omega}) norm of p and u = {del}p. This special subspace does not include the oscillatory near-nullspace components ce{sup ik}({sup {alpha}x+{beta}y)}, where c is a complex vector and where {alpha}{sub 2} + {beta}{sup 2} = 1. These components are eliminated by applying a non-standard coarsening scheme. We achieve this scheme by introducing {open_quotes}ray{close_quotes} basis functions which depend on the parameter pair ({alpha}, {beta}), and which approximate ce{sup ik}({sup {alpha}x+{beta}y)} well on the coarser levels where bilinears cannot. We use several pairs of these parameters on each of these coarser levels so that several coarse grid problems are spun off from the finer levels. Some extensions of this theory to the transverse electric wave solution for Maxwell`s equations will also be 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
2D/1D approximations to the 3D neutron transport equation. II: Numerical comparisons
Kelley, B. W.; Collins, B.; Larsen, E. W.
2013-07-01
In a companion paper [1], (i) several new '2D/1D equations' are introduced as accurate approximations to the 3D Boltzmann transport equation, (ii) the simplest of these approximate equations is systematically discretized, and (iii) a theoretically stable iteration scheme is developed to solve the discrete equations. In this paper, numerical results are presented that confirm the theoretical predictions made in [1]. (authors)
Scattering mean free path in continuous complex media: beyond the Helmholtz equation.
Baydoun, Ibrahim; Baresch, Diego; Pierrat, Romain; Derode, Arnaud
2015-09-01
We present theoretical calculations of the ensemble-averaged (or effective or coherent) wave field propagating in a heterogeneous medium considered as one realization of a random process. In the literature, it is usually assumed that heterogeneity can be accounted for by a random scalar function of the space coordinates, termed the potential. Physically, this amounts to replacing the constant wave speed in Helmholtz' equation by a space-dependent speed. In the case of acoustic waves, we show that this approach leads to incorrect results for the scattering mean free path, no matter how weak the fluctuations. The detailed calculation of the coherent wave field must take into account both a scalar and an operator part in the random potential. When both terms have identical amplitudes, the correct value for the scattering mean free paths is shown to be more than 4 times smaller (13/3, precisely) in the low-frequency limit, whatever the shape of the correlation function. Based on the diagrammatic approach of multiple scattering, theoretical results are obtained for the self-energy and mean free path within Bourret's and on-shell approximations. They are confirmed by numerical experiments. PMID:26465578
The method of polarized traces for the 2D Helmholtz equation
NASA Astrophysics Data System (ADS)
Zepeda-Núñez, Leonardo; Demanet, Laurent
2016-03-01
We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media, with online parallel complexity that scales optimally as O (N/L), where N is the number of volume unknowns, and L is the number of processors, as long as L grows at most like a small fractional power of N. The solver decomposes the domain into layers, and uses transmission conditions in boundary integral form to explicitly define "polarized traces", i.e., up- and down-going waves sampled at interfaces. Local direct solvers are used in each layer to precompute traces of local Green's functions in an embarrassingly parallel way (the offline part), and incomplete Green's formulas are used to propagate interface data in a sweeping fashion, as a preconditioner inside a GMRES loop (the online part). Adaptive low-rank partitioning of the integral kernels is used to speed up their application to interface data. The method uses second-order finite differences. The complexity scalings are empirical but motivated by an analysis of ranks of off-diagonal blocks of oscillatory integrals. They continue to hold in the context of standard geophysical community models such as BP and Marmousi 2, where convergence occurs in 5 to 10 GMRES iterations. While the parallelism in this paper stems from decomposing the domain, we do not explore the alternative of parallelizing the systems solves with distributed linear algebra routines.
A study of domain decomposition methods applied to the discretized Helmholtz equation
NASA Astrophysics Data System (ADS)
Tramel, Robert Wallace
2001-09-01
In this work a domain decomposition based preconditioner of the additive Schwarz type is developed and tested on the linear systems which arise out of the application of the Green's Function/Wave Expansion Discretization. (GFD/WED) method to Helmholtz's equation. In order to develop the additive Schwarz preconditioner, use is made of a class of one-sided Artificial Radiation Boundary Conditions (ARBC) developed during the course of this work. These ARBCs are computationally shown to be quite accurate for use on their own. The ARBC's are used to radiatively couple the various sub-domains which are naturally part of domain decomposition based methods in such a manner as to ensure that the system matrix, when restricted to the sub-domains, is non-singular. In addition, the inter-domain ARBC is constructed such that the solution to the global linear system is unaffected by the presence of the artificial boundaries. The efficacy and efficiency of the method is demonstrated on one, two, and three-dimensional test cases.
Lu, Huancai; Wu, Sean F
2009-03-01
The vibroacoustic responses of a highly nonspherical vibrating object are reconstructed using Helmholtz equation least-squares (HELS) method. The objectives of this study are to examine the accuracy of reconstruction and the impacts of various parameters involved in reconstruction using HELS. The test object is a simply supported and baffled thin plate. The reason for selecting this object is that it represents a class of structures that cannot be exactly described by the spherical Hankel functions and spherical harmonics, which are taken as the basis functions in the HELS formulation, yet the analytic solutions to vibroacoustic responses of a baffled plate are readily available so the accuracy of reconstruction can be checked accurately. The input field acoustic pressures for reconstruction are generated by the Rayleigh integral. The reconstructed normal surface velocities are validated against the benchmark values, and the out-of-plane vibration patterns at several natural frequencies are compared with the natural modes of a simply supported plate. The impacts of various parameters such as number of measurement points, measurement distance, location of the origin of the coordinate system, microphone spacing, and ratio of measurement aperture size to the area of source surface of reconstruction on the resultant accuracy of reconstruction are examined. PMID:19275312
On the Dynamic Programming Approach for the 3D Navier-Stokes Equations
Manca, Luigi
2008-06-15
The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier-Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness argument, existence of solutions for the associated Hamilton-Jacobi-Bellman equation is proved. Finally, existence of an optimal control through the feedback formula and of an optimal state is discussed.
NASA Astrophysics Data System (ADS)
Li, Jingzhi; Liu, Hongyu; Rondi, Luca; Uhlmann, Gunther
2015-04-01
We develop a very general theory on the regularized approximate invisibility cloaking for the wave scattering governed by the Helmholtz equation in any space dimensions via the approach of transformation optics. There are four major ingredients in our proposed theory: (1) The non-singular cloaking medium is obtained by the push-forwarding construction through a transformation that blows up a subset in the virtual space, where is an asymptotic regularization parameter. will degenerate to K 0 as , and in our theory K 0 could be any convex compact set in , or any set whose boundary consists of Lipschitz hypersurfaces, or a finite combination of those sets. (2) A general lossy layer with the material parameters satisfying certain compatibility integral conditions is employed right between the cloaked and cloaking regions. (3) The contents being cloaked could also be extremely general, possibly including, at the same time, generic mediums and, sound-soft, sound-hard and impedance-type obstacles, as well as some sources or sinks. (4) In order to achieve a cloaking device of compact size, particularly for the case when is not "uniformly small", an assembly-by-components, the (ABC) geometry is developed for both the virtual and physical spaces and the blow-up construction is based on concatenating different components. Within the proposed framework, we show that the scattered wave field corresponding to a cloaking problem will converge to u 0 as , with u 0 being the scattered wave field corresponding to a sound-hard K 0. The convergence result is used to theoretically justify the approximate full and partial invisibility cloaks, depending on the geometry of K 0. On the other hand, the convergence results are conducted in a much more general setting than what is needed for the invisibility cloaking, so they are of significant mathematical interest for their own sake. As for applications, we construct three types of full and partial cloaks. Some numerical experiments are
NASA Astrophysics Data System (ADS)
Wu, Haijun; Jiang, Weikang; Zhang, Haibin
2016-07-01
In the procedure of the near-field acoustic holography (NAH) based on the fundamental solutions for Helmholtz equation (FS), the number of FS and the measurement setup to obtain their coefficients are two crucial issues to the successful reconstruction. The current work is motivated to develop a framework for the NAH which supplies a guideline to the determination of the number of FS as well as an optimized measurement setup. A mapping relationship between modes on surfaces of boundary and hologram is analytically derived by adopting the modes as FS in spherical coordinates. Thus, reconstruction is converted to obtain the coefficients of participant modes on holograms. In addition, an integral identity is firstly to be derived for the modes on convex surfaces, which is useful in determining the inefficient or evanescent modes for acoustic radiation in free space. To determine the number of FS adopted in the mapping relationship based NAH (MRS-based NAH), two approaches are proposed to supply reasonable estimations with criteria of point-wise pressure and energy, respectively. A technique to approximate a specific degree of mode on patches by a set of locally orthogonal patterns is explored for three widely used holograms, such as planar, cylindrical and spherical holograms, which results in an automatic determinations of the number and position of experimental setup for a given tolerance. Numerical examples are set up to validate the theory and techniques in the MRS-based NAH. Reconstructions of a cubic model demonstrate the potential of the proposed method for regular models even with corners and shapers. Worse results for the elongated cylinder with two spherical caps reveal the deficiency of the MRS-based NAH for irregular models which is largely due to the adopted modes are FS in spherical coordinates. The NAH framework pursued in the current work provides a new insight to the reconstruction procedure based on the FS in spherical coordinates.
Cauchy's almost forgotten Lagrangian formulation of the Euler equation for 3D incompressible flow
NASA Astrophysics Data System (ADS)
Frisch, Uriel; Villone, Barbara
2014-09-01
Two prized papers, one by Augustin Cauchy in 1815, presented to the French Academy and the other by Hermann Hankel in 1861, presented to Göttingen University, contain major discoveries on vorticity dynamics whose impact is now quickly increasing. Cauchy found a Lagrangian formulation of 3D ideal incompressible flow in terms of three invariants that generalize to three dimensions the now well-known law of conservation of vorticity along fluid particle trajectories for two-dimensional flow. This has very recently been used to prove analyticity in time of fluid particle trajectories for 3D incompressible Euler flow and can be extended to compressible flow, in particular to cosmological dark matter. Hankel showed that Cauchy's formulation gives a very simple Lagrangian derivation of the Helmholtz vorticity-flux invariants and, in the middle of the proof, derived an intermediate result which is the conservation of the circulation of the velocity around a closed contour moving with the fluid. This circulation theorem was to be rediscovered independently by William Thomson (Kelvin) in 1869. Cauchy's invariants were only occasionally cited in the 19th century - besides Hankel, foremost by George Stokes and Maurice Lévy - and even less so in the 20th until they were rediscovered via Emmy Noether's theorem in the late 1960, but reattributed to Cauchy only at the end of the 20th century by Russian scientists.
Implementation of Advanced Two Equation Turbulence Models in the USM3D Unstructured Flow Solver
NASA Technical Reports Server (NTRS)
Wang, Qun-Zhen; Massey, Steven J.; Abdol-Hamid, Khaled S.
2000-01-01
USM3D is a widely-used unstructured flow solver for simulating inviscid and viscous flows over complex geometries. The current version (version 5.0) of USM3D, however, does not have advanced turbulence models to accurately simulate complicated flow. We have implemented two modified versions of the original Jones and Launder k-epsilon "two-equation" turbulence model and the Girimaji algebraic Reynolds stress model in USM3D. Tests have been conducted for three flat plate boundary layer cases, a RAE2822 airfoil and an ONERA M6 wing. The results are compared with those from direct numerical simulation, empirical formulae, theoretical results, and the existing Spalart-Allmaras one-equation model.
Global regular solutions for the 3D Kawahara equation posed on unbounded domains
NASA Astrophysics Data System (ADS)
Larkin, Nikolai A.; Simões, Márcio Hiran
2016-08-01
An initial boundary value problem for the 3D Kawahara equation posed on a channel-type domain was considered. The existence and uniqueness results for global regular solutions as well as exponential decay of small solutions in the H 2-norm were established.
Global regular solutions for the 3D Zakharov-Kuznetsov equation posed on unbounded domains
NASA Astrophysics Data System (ADS)
Larkin, N. A.
2015-09-01
An initial-boundary value problem for the 3D Zakharov-Kuznetsov equation posed on unbounded domains is considered. Existence and uniqueness of a global regular solution as well as exponential decay of the H2-norm for small initial data are proven.
Quasi-regular solutions to a class of 3D degenerating hyperbolic equations
NASA Astrophysics Data System (ADS)
Hristov, T. D.; Popivanov, N. I.; Schneider, M.
2012-11-01
In the fifties M. Protter stated new three-dimensional (3D) boundary value problems (BVP) for mixed type equations of first kind. For hyperbolic-elliptic equations they are multidimensional analogue of the classical two-dimensional (2D) Morawetz-Guderley transonic problem. Up to now, in this case, not a single example of nontrivial solution to the new problem, neither a general existence result is known. The difficulties appear even for BVP in the hyperbolic part of the domain, that were formulated by Protter for weakly hyperbolic equations. In that case the Protter problems are 3D analogues of the plane Darboux or Cauchy-Goursat problems. It is interesting that in contrast to the planar problems the new 3D problems are strongly ill-posed. Some of the Protter problems for degenerating hyperbolic equation without lower order terms or even for the usual wave equation have infinite-dimensional kernels. Therefore there are infinitely many orthogonality conditions for classical solvability of their adjiont problems. So it is interesting to obtain results for uniqueness of solutions adding first order terms in the equation. In the present paper we do this and find conditions for coefficients under which we prove uniqueness of quasi-regular solutions to the Protter problems.
A research of 3D gravity inversion based on the recovery of sparse underdetermined linear equations
NASA Astrophysics Data System (ADS)
Zhaohai, M.
2014-12-01
Because of the properties of gravity data, it is made difficult to solve the problem of multiple solutions. There are two main types of 3D gravity inversion methods：One of two methods is based on the improvement of the instability of the sensitive matrix, solving the problem of multiple solutions and instability in 3D gravity inversion. Another is to join weight function into the 3D gravity inversion iteration. Through constant iteration, it can renewal density values and weight function to achieve the purpose to solve the multiple solutions and instability of the 3D gravity data inversion. Thanks to the sparse nature of the solutions of 3D gravity data inversions, we can transform it into a sparse equation. Then, through solving the sparse equations, we can get perfect 3D gravity inversion results. The main principle is based on zero norm of sparse matrix solution of the equation. Zero norm is mainly to solve the nonzero solution of the sparse matrix. However, the method of this article adopted is same as the principle of zero norm. But the method is the opposite of zero norm to obtain zero value solution. Through the form of a Gaussian fitting solution of the zero norm, we can find the solution by using regularization principle. Moreover, this method has been proved that it had a certain resistance to random noise in the mathematics, and it was more suitable than zero norm for the solution of the geophysical data. 3D gravity which is adopted in this article can well identify abnormal body density distribution characteristics, and it can also recognize the space position of abnormal distribution very well. We can take advantage of the density of the upper and lower limit penalty function to make each rectangular residual density within a reasonable range. Finally, this 3D gravity inversion is applied to a variety of combination model test, such as a single straight three-dimensional model, the adjacent straight three-dimensional model and Y three
NASA Astrophysics Data System (ADS)
Natarajan, Logesh Kumar
This dissertation presents a structure-borne noise analysis technology that is focused on providing a cost-effective noise reduction strategy. Structure-borne sound is generated or transmitted through structural vibration; however, only a small portion of the vibration can effectively produce sound and radiate it to the far-field. Therefore, cost-effective noise reduction is reliant on identifying and suppressing the critical vibration components that are directly responsible for an undesired sound. However, current technologies cannot successfully identify these critical vibration components from the point of view of direct contribution to sound radiation and hence cannot guarantee the best cost-effective noise reduction. The technology developed here provides a strategy towards identifying the critical vibration components and methodically suppressing them to achieve a cost-effective noise reduction. The core of this technology is Helmholtz equation least squares (HELS) based nearfield acoustic holography method. In this study, the HELS formulations derived in spherical co-ordinates using spherical wave expansion functions utilize the input data of acoustic pressures measured in the nearfield of a vibrating object to reconstruct the vibro-acoustic responses on the source surface and acoustic quantities in the far field. Using these formulations, three steps were taken to achieve the goal. First, hybrid regularization techniques were developed to improve the reconstruction accuracy of normal surface velocity of the original HELS method. Second, correlations between the surface vibro-acoustic responses and acoustic radiation were factorized using singular value decomposition to obtain orthogonal basis known here as the forced vibro-acoustic components (F-VACs). The F-VACs enables one to identify the critical vibration components for sound radiation in a similar manner that modal decomposition identifies the critical natural modes in a structural vibration. Finally
The small data solutions of general 3-D quasilinear wave equations. II
NASA Astrophysics Data System (ADS)
Ding, Bingbing; Witt, Ingo; Yin, Huicheng
2016-07-01
This paper is a continuation of the work in [8], where the authors established the global existence of smooth small data solutions to the general 3-D quasilinear wave equation ∑ i , j = 0 3 gij (u , ∂ u) ∂ij2 u = 0 when the weak null condition holds. In the present paper, we show that the smooth small data solutions of equation ∑ i , j = 0 3 gij (u , ∂ u) ∂ij2 u = 0 will blow up in finite time when the weak null condition does not hold and a generic nondegenerate condition on the initial data is satisfied, moreover, a precise blowup time is completely determined. Therefore, collecting the main results in this paper and [8], we have given a basically complete study on the blowup or global existence of small data solutions to the 3-D quasilinear wave equation ∑ i , j = 0 3 gij (u , ∂ u) ∂ij2 u = 0.
Upper Semicontinuity of Pullback Attractors for the 3D Nonautonomous Benjamin-Bona-Mahony Equations
Yang, Xinguang; Wang, Xiaosong; Zhang, Lingrui
2014-01-01
We will study the upper semicontinuity of pullback attractors for the 3D nonautonomouss Benjamin-Bona-Mahony equations with external force perturbation terms. Under some regular assumptions, we can prove the pullback attractors 𝒜 ε(t) of equation ut-Δut-νΔu+∇·F→(u)=ɛg(x,t), x ∈ Ω, converge to the global attractor 𝒜 of the above-mentioned equation with ε = 0 for any t ∈ ℝ. PMID:24790585
NASA Astrophysics Data System (ADS)
Kashirin, A. A.; Smagin, S. I.; Taltykina, M. Yu.
2016-04-01
Interior and exterior three-dimensional Dirichlet problems for the Helmholtz equation are solved numerically. They are formulated as equivalent boundary Fredholm integral equations of the first kind and are approximated by systems of linear algebraic equations, which are then solved numerically by applying an iteration method. The mosaic-skeleton method is used to speed up the solution procedure.
Recasting the 3D Wigner-Liouville equation with spectral components of the force
NASA Astrophysics Data System (ADS)
van de Put, Maarten; Sorée, Bart; Magnus, Wim
The phasespace approach to many-body quantum mechanics, by means of the Wigner-function is interesting through its connection to classical mechanics. Time-evolution of any statistical distribution of states under influence of a (time-dependent) Hamiltonian is obtained through use of the Wigner-Liouville equation. The standard form of this equation contains two 3D integrals, over the entire phase space. As a result, this form emphasizes the non-locality of the interaction of the potential, but lacks simplicity and ease of understanding. Furthermore, the integrals make numerical solution of the Wigner-Liouville equation challenging. We present an alternative form to the Wigner-Liouville equation based on the force rather than the potential, in alignment with the classical Boltzmann equation. Decomposition of the force in its spectral components yields a simpler form of the Wigner-Liouville equation. This new form has only one 3D integral over the spectral force components, and is local in position, simplifying both interpretation and numerical implementation. Because of its use of the force, it straightforwardly reduces to the Boltzmann equation under classical conditions.
Ciraolo, Giulio Gargano, Francesco Sciacca, Vincenzo
2013-08-01
We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.
Equation-of-State Test Suite for the DYNA3D Code
Benjamin, Russell D.
2015-11-05
This document describes the creation and implementation of a test suite for the Equationof- State models in the DYNA3D code. A customized input deck has been created for each model, as well as a script that extracts the relevant data from the high-speed edit file created by DYNA3D. Each equation-of-state model is broken apart and individual elements of the model are tested, as well as testing the entire model. The input deck for each model is described and the results of the tests are discussed. The intent of this work is to add this test suite to the validation suite presently used for DYNA3D.
Xiong, Z.; Tripp, A.C.
1994-12-31
This paper presents an integral equation algorithm for 3D EM modeling at high frequencies for applications in engineering an environmental studies. The integral equation method remains the same for low and high frequencies, but the dominant roles of the displacements currents complicate both numerical treatments and interpretations. With singularity extraction technique they successively extended the application of the Hankel filtering technique to the computation of Hankel integrals occurring in high frequency EM modeling. Time domain results are calculated from frequency domain results via Fourier transforms. While frequency domain data are not obvious for interpretations, time domain data show wave-like pictures that resemble seismograms. Both 1D and 3D numerical results show clearly the layer interfaces.
NuSol - Numerical solver for the 3D stationary nuclear Schrödinger equation
NASA Astrophysics Data System (ADS)
Graen, Timo; Grubmüller, Helmut
2016-01-01
The classification of short hydrogen bonds depends on several factors including the shape and energy spacing between the nuclear eigenstates of the hydrogen. Here, we describe the NuSol program in which three classes of algorithms were implemented to solve the 1D, 2D and 3D time independent nuclear Schrödinger equation. The Schrödinger equation was solved using the finite differences based Numerov's method which was extended to higher dimensions, the more accurate pseudo-spectral Chebyshev collocation method and the sinc discrete variable representation by Colbert and Miller. NuSol can be applied to solve the Schrödinger equation for arbitrary analytical or numerical potentials with focus on nuclei bound by the potential of their molecular environment. We validated the methods against literature values for the 2D Henon-Heiles potential, the 3D linearly coupled sextic oscillators and applied them to study hydrogen bonding in the malonaldehyde derivate 4-cyano-2,2,6,6-tetramethyl-3,5-heptanedione. With NuSol, the extent of nuclear delocalization in a given molecular potential can directly be calculated without relying on linear reaction coordinates in 3D molecular space.
Some Properties of the M3D-C1 Form of the 3D Magnetohydrodynamics Equations
J. Breslau, N. Ferraro, S. Jardin
2009-07-10
We introduce a set of scalar variables and projection operators for the vector momentum and magnetic field evolution equations that have several unique and desirable properties, making them a preferred system for solving the magnetohydrodynamics equations in a torus with a strong toroidal magnetic field. We derive a "weak form" of these equations that explicitly conserves energy and is suitable for a Galerkin finite element formulation provided the basis elements have C1 continuity. Systems of reduced equations are discussed, along with their energy conservation properties. An implicit time advance is presented that adds diagonally dominant self-adjoint energy terms to the mass matrix to obtain numerical stability.
Benchmarks of 3D Laplace Equation Solvers in a Cubic Configuration for Streamer Simulation
NASA Astrophysics Data System (ADS)
Joseph-Marie, Plewa; Olivier, Ducasse; Philippe, Dessante; Carolyn, Jacobs; Olivier, Eichwald; Nicolas, Renon; Mohammed, Yousfi
2016-05-01
The aim of this paper is to test a developed SOR R&B method using the Chebyshev accelerator algorithm to solve the Laplace equation in a cubic 3D configuration. Comparisons are made in terms of precision and computing time with other elliptic equation solvers proposed in the open source LIS library. The first results, obtained by using a single core on a HPC, show that the developed SOR R&B method is efficient when the spectral radius needed for the Chebyshev acceleration is carefully pre-estimated. Preliminary results obtained with a parallelized code using the MPI library are also discussed when the calculation is distributed over one hundred cores.
Analytical and numerical aspects in solving the controlled 3D Gross-Pitaevskii equation
Fedele, R.; Jovanovic, D.; De Nicola, S.; Eliasson, B.; Shukla, P. K.
2009-11-10
The results of recently developed investigations, that have been carried out within the framework of the controlling potential method (CPM), are reviewed. This method allows one to decompose a three dimensional (3D) Gross-Pitaevskii equation (GPE) into the pair of coupled Schroedinger-type equations. Under suitable mathematical conditions, the solutions of the 3D controlled GPE can be constructed from the solutions of a 2D linear Schroedinger equation (the transverse component of the GPE) coupled with a 1D nonlinear Schroedinger equation (the longitudinal component of the GPE). Such decomposition allows one to cast the solutions in the form of the product of the solutions of the transverse and the longitudinal components of the GPE. The coupling between these two equations is the functional of both the transverse and the longitudinal profiles. It is shown that the CPM can be used to obtain a new class of three-dimensional solitary waves solutions of the GPE, which governs the dynamics of Bose-Einstein condensates. By imposing an external controlling potential, the desired time-dependent shape of the localized BECs is obtained. The stability of the exact solutions was checked with direct simulations of the time -dependent, three-dimensional GPE. Our simulations show that the localized condensates are stable with respect to perturbed initial conditions.
A least-squares finite element method for 3D incompressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Lin, T. L.; Hou, Lin-Jun; Povinelli, Louis A.
1993-01-01
The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.
NASA Technical Reports Server (NTRS)
Zhong, W. F.; Fu, L. S.
1983-01-01
Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) + alpha(2), for the cases of a finite cylindrical region and a region of rectangular parallelepiped. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r r' and r 4', where r and r' are distances from the origin to the point of observation and source, respectively. When the wave number approaches zero, the results reduce directly to the potentials of variable densities.
A novel numerical flux for the 3D Euler equations with general equation of state
NASA Astrophysics Data System (ADS)
Toro, Eleuterio F.; Castro, Cristóbal E.; Lee, Bok Jik
2015-12-01
Here we extend the flux vector splitting approach recently proposed in E.F. Toro and M.E. Vázquez-Cendón (2012) [42]. The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both space and time through application of the semi-discrete ADER methodology on general meshes. The resulting methods are systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems. Formal high accuracy is assessed through convergence rates studies for schemes of up to 4th order of accuracy in both space and time on unstructured meshes.
A 3D GCL compatible cell-centered Lagrangian scheme for solving gas dynamics equations
NASA Astrophysics Data System (ADS)
Georges, Gabriel; Breil, Jérôme; Maire, Pierre-Henri
2016-01-01
Solving the gas dynamics equations under the Lagrangian formalism enables to simulate complex flows with strong shock waves. This formulation is well suited to the simulation of multi-material compressible fluid flows such as those encountered in the domain of High Energy Density Physics (HEDP). These types of flows are characterized by complex 3D structures such as hydrodynamic instabilities (Richtmyer-Meshkov, Rayleigh-Taylor, etc.). Recently, the 3D extension of different Lagrangian schemes has been proposed and appears to be challenging. More precisely, the definition of the cell geometry in the 3D space through the treatment of its non-planar faces and the limiting of a reconstructed field in 3D in the case of a second-order extension are of great interest. This paper proposes two new methods to solve these problems. A systematic and symmetric geometrical decomposition of polyhedral cells is presented. This method enables to define a discrete divergence operator leading to the respect of the Geometric Conservation Law (GCL). Moreover, a multi-dimensional minmod limiter is proposed. This new limiter constructs, from nodal gradients, a cell gradient which enables to ensure the monotonicity of the numerical solution even in presence of strong discontinuity. These new ingredients are employed into a cell-centered Lagrangian scheme. Robustness and accuracy are assessed against various representative test cases.
A fast rebinning algorithm for 3D positron emission tomography using John's equation
NASA Astrophysics Data System (ADS)
Defrise, Michel; Liu, Xuan
1999-08-01
Volume imaging in positron emission tomography (PET) requires the inversion of the three-dimensional (3D) x-ray transform. The usual solution to this problem is based on 3D filtered-backprojection (FBP), but is slow. Alternative methods have been proposed which factor the 3D data into independent 2D data sets corresponding to the 2D Radon transforms of a stack of parallel slices. Each slice is then reconstructed using 2D FBP. These so-called rebinning methods are numerically efficient but are approximate. In this paper a new exact rebinning method is derived by exploiting the fact that the 3D x-ray transform of a function is the solution to the second-order partial differential equation first studied by John. The method is proposed for two sampling schemes, one corresponding to a pair of infinite plane detectors and another one corresponding to a cylindrical multi-ring PET scanner. The new FORE-J algorithm has been implemented for this latter geometry and was compared with the approximate Fourier rebinning algorithm FORE and with another exact rebinning algorithm, FOREX. Results with simulated data demonstrate a significant improvement in accuracy compared to FORE, while the reconstruction time is doubled. Compared to FOREX, the FORE-J algorithm is slightly less accurate but more than three times faster.
Shao, Yan-Lin Faltinsen, Odd M.
2014-10-01
We propose a new efficient and accurate numerical method based on harmonic polynomials to solve boundary value problems governed by 3D Laplace equation. The computational domain is discretized by overlapping cells. Within each cell, the velocity potential is represented by the linear superposition of a complete set of harmonic polynomials, which are the elementary solutions of Laplace equation. By its definition, the method is named as Harmonic Polynomial Cell (HPC) method. The characteristics of the accuracy and efficiency of the HPC method are demonstrated by studying analytical cases. Comparisons will be made with some other existing boundary element based methods, e.g. Quadratic Boundary Element Method (QBEM) and the Fast Multipole Accelerated QBEM (FMA-QBEM) and a fourth order Finite Difference Method (FDM). To demonstrate the applications of the method, it is applied to some studies relevant for marine hydrodynamics. Sloshing in 3D rectangular tanks, a fully-nonlinear numerical wave tank, fully-nonlinear wave focusing on a semi-circular shoal, and the nonlinear wave diffraction of a bottom-mounted cylinder in regular waves are studied. The comparisons with the experimental results and other numerical results are all in satisfactory agreement, indicating that the present HPC method is a promising method in solving potential-flow problems. The underlying procedure of the HPC method could also be useful in other fields than marine hydrodynamics involved with solving Laplace equation.
Efficient solution on solving 3D Maxwell equations using stable semi-implicit splitting method
NASA Astrophysics Data System (ADS)
Cen, Wei; Gu, Ning
2016-05-01
In this paper, we propose an efficient solution on solving 3-dimensional (3D) time-domain Maxwell equations using the semi-implicit Crank-Nicholson (CN) method for time domain discretization with advantage of unconditional time stability. By applying the idea of fractional steps method (FSM) to the CN scheme, the proposed method provides a much simpler and efficient implementation than a direct implementation of the CN scheme. Compared with the alternating-direction implicit (ADI) method and explicit finite-difference time-domain approach (FDTD), it significantly saves the computational resource like memory and CPU time while remains similar numerical accuracy.
The Dirichlet problem for the two-dimensional Helmholtz equation for an open boundary
NASA Technical Reports Server (NTRS)
Hayashi, Y.
1973-01-01
Development of a complete theory of the two-dimensional Dirichlet problem for an open boundary. It is shown that the solution of the Dirichlet problem for an open boundary requires the solution of a Fredholm integral equation of the first kind. Although a Fredholm integral equation of the first kind usually has no solution if the kernel is continuous, owing to the logarithmic singularity of the kernel, the equation in this case is converted to a singular integral equation with a Cauchy kernel. It is proven that the homogeneous adjoint equation of the singular integral equation has no nonzero solution. By virtue of this result, and with the aid of an existence theorem known in the theory of singular integral equations, the existence of solutions of the singular integral equation, and then of the unique solution of the Fredholm integral equation of the first kind is proved.
Fast and Robust Sixth Order Multigrid Computation for 3D Convection Diffusion Equation.
Wang, Yin; Zhang, Jun
2010-10-15
We present a sixth order explicit compact finite difference scheme to solve the three dimensional (3D) convection diffusion equation. We first use multiscale multigrid method to solve the linear systems arising from a 19-point fourth order discretization scheme to compute the fourth order solutions on both the coarse grid and the fine grid. Then an operator based interpolation scheme combined with an extrapolation technique is used to approximate the sixth order accurate solution on the fine grid. Since the multigrid method using a standard point relaxation smoother may fail to achieve the optimal grid independent convergence rate for solving convection diffusion equation with a high Reynolds number, we implement the plane relaxation smoother in the multigrid solver to achieve better grid independency. Supporting numerical results are presented to demonstrate the efficiency and accuracy of the sixth order compact scheme (SOC), compared with the previously published fourth order compact scheme (FOC). PMID:21151737
A CNN-based approach to integrate the 3-D turbolent diffusion equation
NASA Astrophysics Data System (ADS)
Nunnari, G.
2003-04-01
The paper deals with the integration of the 3-D turbulent diffusion equation. This problem is relevant in several application fields including fluid dynamics, air/water pollution, volcanic ash emissions and industrial hazard assessment. As it is well known numerical solution of such a kind of equation is very time consuming even by using modern digital computers and this represents a short-coming for on-line applications. To overcome this drawback a Cellular Neural Network Approach is proposed in this paper. CNN's proposed by Chua and Yang in 1988 are massive parallel analog non-linear circuits with local interconnections between the computing elements that allow very fast distributed computations. Nowadays several producers of semiconductors such as SGS-Thomson are producing on chip CNN's so that their massive use for heavy computing applications is expected in the near future. In the paper the methodological background of the proposed approach will be outlined. Further some results both in terms of accuracy and computation time will be presented also in comparison with traditional three-dimensional computation schemes. Some results obtained to model 3-D pollution problems in the industrial area of Siracusa (Italy), characterised by a large concentration of petrol-chemical plants, will be presented.
New equations to calculate 3D joint centres in the lower extremities.
Sandau, Martin; Heimbürger, Rikke V; Villa, Chiara; Jensen, Karl E; Moeslund, Thomas B; Aanæs, Henrik; Alkjær, Tine; Simonsen, Erik B
2015-10-01
Biomechanical movement analysis in 3D requires estimation of joint centres in the lower extremities and this estimation is based on extrapolation from markers placed on anatomical landmarks. The purpose of the present study was to quantify the accuracy of three established set of equations and provide new improved equations to predict the joint centre locations. The 'true' joint centres of the knee and ankle joint were obtained in vivo by MRI scans on 10 male subjects whereas the 'true' hip joint centre was obtained in 10 male and 10 female cadavers by CT scans. For the hip joint the errors ranged from 26.7 (8.9) to 29.6 (7.5) mm, for the knee joint 5.8 (3.1) to 22.6 (3.3) mm and for the ankle joint 14.4 (2.2) to 27.0 (4.6) mm. This differed significantly from the improved equations by which the error for the hip joint ranged from 8.2 (3.6) to 11.6 (5.6) mm, for the knee joint from 2.9 (2.1) to 4.7 (2.5) mm and for the ankle joint from 3.4 (1.3) to 4.1 (2.0) mm. The coefficients in the new hip joint equations differed significantly between sexes. This difference depends on anatomical differences of the male and female pelvis. PMID:26320760
NASA Astrophysics Data System (ADS)
Chen, Duan; Cai, Wei; Zinser, Brian; Cho, Min Hyung
2016-09-01
In this paper, we develop an accurate and efficient Nyström volume integral equation (VIE) method for the Maxwell equations for a large number of 3-D scatterers. The Cauchy Principal Values that arise from the VIE are computed accurately using a finite size exclusion volume together with explicit correction integrals consisting of removable singularities. Also, the hyper-singular integrals are computed using interpolated quadrature formulae with tensor-product quadrature nodes for cubes, spheres and cylinders, that are frequently encountered in the design of meta-materials. The resulting Nyström VIE method is shown to have high accuracy with a small number of collocation points and demonstrates p-convergence for computing the electromagnetic scattering of these objects. Numerical calculations of multiple scatterers of cubic, spherical, and cylindrical shapes validate the efficiency and accuracy of the proposed method.
Cari, C. Suparmi, A.
2014-09-30
Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.
An unstaggered constrained transport method for the 3D ideal magnetohydrodynamic equations
NASA Astrophysics Data System (ADS)
Helzel, Christiane; Rossmanith, James A.; Taetz, Bertram
2011-05-01
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discrete divergence of the magnetic field, or else be faced with nonlinear numerical instabilities. One approach for controlling the discrete divergence is through a so-called constrained transport method, which is based on first predicting a magnetic field through a standard finite volume solver, and then correcting this field through the appropriate use of a magnetic vector potential. In this work we develop a constrained transport method for the 3D ideal MHD equations that is based on a high-resolution wave propagation scheme. Our proposed scheme is the 3D extension of the 2D scheme developed by Rossmanith [J.A. Rossmanith, An unstaggered, high-resolution constrained transport method for magnetohydrodynamic flows, SIAM J. Sci. Comput. 28 (2006) 1766], and is based on the high-resolution wave propagation method of Langseth and LeVeque [J.O. Langseth, R.J. LeVeque, A wave propagation method for threedimensional hyperbolic conservation laws, J. Comput. Phys. 165 (2000) 126]. In particular, in our extension we take great care to maintain the three most important properties of the 2D scheme: (1) all quantities, including all components of the magnetic field and magnetic potential, are treated as cell-centered; (2) we develop a high-resolution wave propagation scheme for evolving the magnetic potential; and (3) we develop a wave limiting approach that is applied during the vector potential evolution, which controls unphysical oscillations in the magnetic field. One of the key numerical difficulties that is novel to 3D is that the transport equation that must be solved for the magnetic vector potential is only weakly hyperbolic. In presenting our numerical algorithm we describe how to numerically handle this problem of weak hyperbolicity, as well as how to choose an appropriate gauge condition. The
Computational time analysis of the numerical solution of 3D electrostatic Poisson's equation
NASA Astrophysics Data System (ADS)
Kamboh, Shakeel Ahmed; Labadin, Jane; Rigit, Andrew Ragai Henri; Ling, Tech Chaw; Amur, Khuda Bux; Chaudhary, Muhammad Tayyab
2015-05-01
3D Poisson's equation is solved numerically to simulate the electric potential in a prototype design of electrohydrodynamic (EHD) ion-drag micropump. Finite difference method (FDM) is employed to discretize the governing equation. The system of linear equations resulting from FDM is solved iteratively by using the sequential Jacobi (SJ) and sequential Gauss-Seidel (SGS) methods, simulation results are also compared to examine the difference between the results. The main objective was to analyze the computational time required by both the methods with respect to different grid sizes and parallelize the Jacobi method to reduce the computational time. In common, the SGS method is faster than the SJ method but the data parallelism of Jacobi method may produce good speedup over SGS method. In this study, the feasibility of using parallel Jacobi (PJ) method is attempted in relation to SGS method. MATLAB Parallel/Distributed computing environment is used and a parallel code for SJ method is implemented. It was found that for small grid size the SGS method remains dominant over SJ method and PJ method while for large grid size both the sequential methods may take nearly too much processing time to converge. Yet, the PJ method reduces computational time to some extent for large grid sizes.
NASA Technical Reports Server (NTRS)
Yokota, Jeffrey W.
1988-01-01
An LU implicit multigrid algorithm is developed to calculate 3-D compressible viscous flows. This scheme solves the full 3-D Reynolds-Averaged Navier-Stokes equation with a two-equation kappa-epsilon model of turbulence. The flow equations are integrated by an efficient, diagonally inverted, LU implicit multigrid scheme while the kappa-epsilon equations are solved, uncoupled from the flow equations, by a block LU implicit algorithm. The flow equations are solved within the framework of the multigrid method using a four-grid level W-cycle, while the kappa-epsilon equations are iterated only on the finest grid. This treatment of the Reynolds-Averaged Navier-Stokes equations proves to be an efficient method for calculating 3-D compressible viscous flows.
NASA Technical Reports Server (NTRS)
Grosse, Ralf
1990-01-01
Propagation of sound through the turbulent atmosphere is a statistical problem. The randomness of the refractive index field causes sound pressure fluctuations. Although no general theory to predict sound pressure statistics from given refractive index statistics exists, there are several approximate solutions to the problem. The most common approximation is the parabolic equation method. Results obtained by this method are restricted to small refractive index fluctuations and to small wave lengths. While the first condition is generally met in the atmosphere, it is desirable to overcome the second. A generalization of the parabolic equation method with respect to the small wave length restriction is presented.
NASA Astrophysics Data System (ADS)
Chapman, Alexander Lloyd
Recently, a sound source identification technique called CRAFT was developed as an advance in the state of the art in inverse noise problems. It addressed some limitations associated with nearfield acoustic holography and a few of the issues with inverse boundary element method. This work centers on two critical issues associated with the CRAFT algorithm. Although CRAFT employs the complete general solution associated with the Helmholtz equation, the approach taken to derive those equations results in computational inefficiency when implemented numerically. In this work, a mathematical approach to derivation of the basis equations results in a doubling in efficiency. This formulation of CRAFT is termed general Helmholtz equation, least-squares method (GEN-HELS). Additionally, the numerous singular points present in the gradient of the basis functions are shown here to resolve to finite limits. As a realistic test case, a diesel engine surface pressure and velocity are reconstructed to show the increase in efficiency from CRAFT to GEN-HELS. Keywords: Inverse Numerical Acoustics, Acoustic Holography, Helmholtz Equation, HELS Method, CRAFT Algorithm.
An iterative KP1 method for solving the transport equation in 3D domains on unstructured grids
NASA Astrophysics Data System (ADS)
Kokonkov, N. I.; Nikolaeva, O. V.
2015-10-01
A two-step iterative KP1 method for solving systems of grid equations that approximate the integro-differential transport equation in 3D domains on unstructured grids using nodal SN methods is described. Results of testing the efficiency of the proposed method in solving benchmark problems of reactor protection on tetrahedral grids are presented.
Efficient 3D/1D self-consistent integral-equation analysis of ICRH antennae
NASA Astrophysics Data System (ADS)
Maggiora, R.; Vecchi, G.; Lancellotti, V.; Kyrytsya, V.
2004-08-01
This work presents a comprehensive account of the theory and implementation of a method for the self-consistent numerical analysis of plasma-facing ion-cyclotron resonance heating (ICRH) antenna arrays. The method is based on the integral-equation formulation of the boundary-value problem, solved via a weighted-residual scheme. The antenna geometry (including Faraday shield bars and a recess box) is fairly general and three-dimensional (3D), and the plasma is in the one-dimensional (1D) 'slab' approximation; finite-Larmor radius effects, as well as plasma density and temperature gradients, are considered. Feeding via the voltages in the access coaxial lines is self-consistently accounted throughout and the impedance or scattering matrix of the antenna array obtained therefrom. The problem is formulated in both the dual space (physical) and spectral (wavenumber) domains, which allows the extraction and simple handling of the terms that slow the convergence in the spectral domain usually employed. This paper includes validation tests of the developed code against measured data, both in vacuo and in the presence of plasma. An example of application to a complex geometry is also given.
NASA Astrophysics Data System (ADS)
Abdi, Daniel S.; Giraldo, Francis X.
2016-09-01
A unified approach for the numerical solution of the 3D hyperbolic Euler equations using high order methods, namely continuous Galerkin (CG) and discontinuous Galerkin (DG) methods, is presented. First, we examine how classical CG that uses a global storage scheme can be constructed within the DG framework using constraint imposition techniques commonly used in the finite element literature. Then, we implement and test a simplified version in the Non-hydrostatic Unified Model of the Atmosphere (NUMA) for the case of explicit time integration and a diagonal mass matrix. Constructing CG within the DG framework allows CG to benefit from the desirable properties of DG such as, easier hp-refinement, better stability etc. Moreover, this representation allows for regional mixing of CG and DG depending on the flow regime in an area. The different flavors of CG and DG in the unified implementation are then tested for accuracy and performance using a suite of benchmark problems representative of cloud-resolving scale, meso-scale and global-scale atmospheric dynamics. The value of our unified approach is that we are able to show how to carry both CG and DG methods within the same code and also offer a simple recipe for modifying an existing CG code to DG and vice versa.
A remark on the Beale-Kato-Majda criterion for the 3D MHD equations with zero magnetic diffusivity
NASA Astrophysics Data System (ADS)
Gala, Sadek; Ragusa, Maria Alessandra
2016-06-01
In this work, we show that a smooth solution of the 3D MHD equations with zero magnetic diffusivity in the whole space ℝ3 breaks down if and only if a certain norm of the magnetic field blows up at the same time.
Solution of the Skyrme HF + BCS equation on a 3D mesh
NASA Astrophysics Data System (ADS)
Bonche, P.; Flocard, H.; Heenen, P. H.
2005-09-01
Over the years, the ev8 code has been a very useful tool for the study of nuclear mean-field theory. Its main characteristic is that it solves the Hartree-Fock plus BCS equations for Skyrme type functionals via a discretization of the individual wave-functions on a three-dimensional Cartesian mesh. This allows maximal flexibility in the determination of the nuclear shape by the variational process. For instance, the same mesh can be used to describe the oblate deformed, spherical, prolate deformed, superdeformed and fission configurations of a given nucleus. The quadrupole constraining operator yielding the deformation energy curve covering all these configurations is included in ev8. This version of the code is restricted to even-even nuclei. Program summaryTitle of program:ev8 Catalogue identifier:ADWA Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWA Licensing provisions: none Computers on which the program has been tested: HP-RX4640, Compaq-Digital Alpha GS140, has run on several other platforms Computer for which the program is designed and others on which is has been tested:Unix, Linux Operating systems or monitors under which the program has been tested:FORTRAN-90 Programming language used:depends on problem; example given requires 60 MB Memory required to execute with typical data:yes No. of lines in distributed program, including test data, etc.:11 524 No. of bytes in distributed program, including test data, etc.:89 949 Distribution format:tar.gzip file Nature of the physical problem:By means of the Hartree-Fock plus BCS method using Skyrme type functionals, ev8 allows a study of the evolution of the binding energy of even-even nuclei for various shapes determined by the most general quadrupole constraint. Solution method:The program expands the single-particle wave-functions on a 3D Cartesian mesh. The nonlinear mean-field equations are solved by the
On the Global Regularity of a Helical-Decimated Version of the 3D Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Biferale, Luca; Titi, Edriss S.
2013-06-01
We study the global regularity, for all time and all initial data in H 1/2, of a recently introduced decimated version of the incompressible 3D Navier-Stokes (dNS) equations. The model is based on a projection of the dynamical evolution of Navier-Stokes (NS) equations into the subspace where helicity (the L 2-scalar product of velocity and vorticity) is sign-definite. The presence of a second (beside energy) sign-definite inviscid conserved quadratic quantity, which is equivalent to the H 1/2-Sobolev norm, allows us to demonstrate global existence and uniqueness, of space-periodic solutions, together with continuity with respect to the initial conditions, for this decimated 3D model. This is achieved thanks to the establishment of two new estimates, for this 3D model, which show that the H 1/2 and the time average of the square of the H 3/2 norms of the velocity field remain finite. Such two additional bounds are known, in the spirit of the work of H. Fujita and T. Kato (Arch. Ration. Mech. Anal. 16:269-315, 1964; Rend. Semin. Mat. Univ. Padova 32:243-260, 1962), to be sufficient for showing well-posedness for the 3D NS equations. Furthermore, they are directly linked to the helicity evolution for the dNS model, and therefore with a clear physical meaning and consequences.
Finite Element Code For 3D-Hydraulic Fracture Propagation Equations (3-layer).
Energy Science and Technology Software Center (ESTSC)
1992-03-24
HYFRACP3D is a finite element program for simulation of a pseudo three-dimensional fracture geometries with a two-dimensional planar solution. The model predicts the height, width and winglength over time for a hydraulic fracture propagating in a three-layered system of rocks with variable rock mechanics properties.
NASA Astrophysics Data System (ADS)
Zhdanov, M. S.; Cuma, M.; Black, N.; Wilson, G. A.
2009-12-01
The marine controlled source electromagnetic (MCSEM) method has become widely used in offshore oil and gas exploration. Interpretation of MCSEM data is still a very challenging problem, especially if one would like to take into account the realistic 3D structure of the subsurface. The inversion of MCSEM data is complicated by the fact that the EM response of a hydrocarbon-bearing reservoir is very weak in comparison with the background EM fields generated by an electric dipole transmitter in complex geoelectrical structures formed by a conductive sea-water layer and the terranes beneath it. In this paper, we present a review of the recent developments in the area of large-scale 3D EM forward modeling and inversion. Our approach is based on using a new integral form of Maxwell’s equations allowing for an inhomogeneous background conductivity, which results in a numerically effective integral representation for 3D EM field. This representation provides an efficient tool for the solution of 3D EM inverse problems. To obtain a robust inverse model of the conductivity distribution, we apply regularization based on a focusing stabilizing functional which allows for the recovery of models with both smooth and sharp geoelectrical boundaries. The method is implemented in a fully parallel computer code, which makes it possible to run large-scale 3D inversions on grids with millions of inversion cells. This new technique can be effectively used for active EM detection and monitoring of the subsurface targets.
On the transition towards slow manifold in shallow-water and 3D Euler equations in a rotating frame
NASA Technical Reports Server (NTRS)
Mahalov, A.
1994-01-01
The long-time, asymptotic state of rotating homogeneous shallow-water equations is investigated. Our analysis is based on long-time averaged rotating shallow-water equations describing interactions of large-scale, horizontal, two-dimensional motions with surface inertial-gravity waves field for a shallow, uniformly rotating fluid layer. These equations are obtained in two steps: first by introducing a Poincare/Kelvin linear propagator directly into classical shallow-water equations, then by averaging. The averaged equations describe interaction of wave fields with large-scale motions on time scales long compared to the time scale 1/f(sub o) introduced by rotation (f(sub o)/2-angular velocity of background rotation). The present analysis is similar to the one presented by Waleffe (1991) for 3D Euler equations in a rotating frame. However, since three-wave interactions in rotating shallow-water equations are forbidden, the final equations describing the asymptotic state are simplified considerably. Special emphasis is given to a new conservation law found in the asymptotic state and decoupling of the dynamics of the divergence free part of the velocity field. The possible rising of a decoupled dynamics in the asymptotic state is also investigated for homogeneous turbulence subjected to a background rotation. In our analysis we use long-time expansion, where the velocity field is decomposed into the 'slow manifold' part (the manifold which is unaffected by the linear 'rapid' effects of rotation or the inertial waves) and a formal 3D disturbance. We derive the physical space version of the long-time averaged equations and consider an invariant, basis-free derivation. This formulation can be used to generalize Waleffe's (1991) helical decomposition to viscous inhomogeneous flows (e.g. problems in cylindrical geometry with no-slip boundary conditions on the cylinder surface and homogeneous in the vertical direction).
Xie, G.; Li, J.; Majer, E.; Zuo, D.
1998-07-01
This paper describes a new 3D parallel GILD electromagnetic (EM) modeling and nonlinear inversion algorithm. The algorithm consists of: (a) a new magnetic integral equation instead of the electric integral equation to solve the electromagnetic forward modeling and inverse problem; (b) a collocation finite element method for solving the magnetic integral and a Galerkin finite element method for the magnetic differential equations; (c) a nonlinear regularizing optimization method to make the inversion stable and of high resolution; and (d) a new parallel 3D modeling and inversion using a global integral and local differential domain decomposition technique (GILD). The new 3D nonlinear electromagnetic inversion has been tested with synthetic data and field data. The authors obtained very good imaging for the synthetic data and reasonable subsurface EM imaging for the field data. The parallel algorithm has high parallel efficiency over 90% and can be a parallel solver for elliptic, parabolic, and hyperbolic modeling and inversion. The parallel GILD algorithm can be extended to develop a high resolution and large scale seismic and hydrology modeling and inversion in the massively parallel computer.
A lattice-Boltzmann scheme of the Navier-Stokes equations on a 3D cuboid lattice
NASA Astrophysics Data System (ADS)
Min, Haoda; Peng, Cheng; Wang, Lian-Ping
2015-11-01
The standard lattice-Boltzmann method (LBM) for fluid flow simulation is based on a square (in 2D) or cubic (in 3D) lattice grids. Recently, two new lattice Boltzmann schemes have been developed on a 2D rectangular grid using the MRT (multiple-relaxation-time) collision model, by adding a free parameter in the definition of moments or by extending the equilibrium moments. Here we developed a lattice Boltzmann model on 3D cuboid lattice, namely, a lattice grid with different grid lengths in different spatial directions. We designed our MRT-LBM model by matching the moment equations from the Chapman-Enskog expansion with the Navier-Stokes equations. The model guarantees correct hydrodynamics. A second-order term is added to the equilibrium moments in order to restore the isotropy of viscosity on a cuboid lattice. The form and the coefficients of the extended equilibrium moments are determined through an inverse design process. An additional benefit of the model is that the viscosity can be adjusted independent of the stress-moment relaxation parameter, thus improving the numerical stability of the model. The resulting cuboid MRT-LBM model is then validated through benchmark simulations using laminar channel flow, turbulent channel flow, and the 3D Taylor-Green vortex flow.
Numerical solution of 3D Navier-Stokes equations with upwind implicit schemes
NASA Technical Reports Server (NTRS)
Marx, Yves P.
1990-01-01
An upwind MUSCL type implicit scheme for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions schemes on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind schemes. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.
NASA Astrophysics Data System (ADS)
Chatterjee, Kausik
2016-06-01
The objective of this paper is the extension and application of a newly-developed Green's function Monte Carlo (GFMC) algorithm to the estimation of the derivative of the solution of the one-dimensional (1D) Helmholtz equation subject to Neumann and mixed boundary conditions problems. The traditional GFMC approach for the solution of partial differential equations subject to these boundary conditions involves "reflecting boundaries" resulting in relatively large computational times. My work, inspired by the work of K.K. Sabelfeld is philosophically different in that there is no requirement for reflection at these boundaries. The underlying feature of this algorithm is the elimination of the use of reflecting boundaries through the use of novel Green's functions that mimic the boundary conditions of the problem of interest. My past work has involved the application of this algorithm to the estimation of the solution of the 1D Laplace equation, the Helmholtz equation and the modified Helmholtz equation. In this work, this algorithm has been adapted to the estimation of the derivative of the solution which is a very important development. In the traditional approach involving reflection, to estimate the derivative at a certain number of points, one has to a priori estimate the solution at a larger number of points. In the case of a one-dimensional problem for instance, to obtain the derivative of the solution at a point, one has to obtain the solution at two points, one on each side of the point of interest. These points have to be close enough so that the validity of the first-order approximation for the derivative operator is justified and at the same time, the actual difference between the solutions at these two points has to be at least an order of magnitude higher than the statistical error in the estimation of the solution, thus requiring a significantly larger number of random-walks than that required for the estimation of the solution. In this new approach
On Energy Cascades in the Forced 3D Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Dascaliuc, R.; Grujić, Z.
2016-02-01
We show—in the framework of physical scales and (K_1,K_2) -averages—that Kolmogorov's dissipation law combined with the smallness condition on a Taylor length scale is sufficient to guarantee energy cascades in the forced Navier-Stokes equations. Moreover, in the periodic case we establish restrictive scaling laws—in terms of Grashof number—for kinetic energy, energy flux, and energy dissipation rate. These are used to improve our sufficient condition for forced cascades in physical scales.
On Energy Cascades in the Forced 3D Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Dascaliuc, R.; Grujić, Z.
2016-06-01
We show—in the framework of physical scales and (K_1,K_2)-averages—that Kolmogorov's dissipation law combined with the smallness condition on a Taylor length scale is sufficient to guarantee energy cascades in the forced Navier-Stokes equations. Moreover, in the periodic case we establish restrictive scaling laws—in terms of Grashof number—for kinetic energy, energy flux, and energy dissipation rate. These are used to improve our sufficient condition for forced cascades in physical scales.
Calculations of separated 3-D flows with a pressure-staggered Navier-Stokes equations solver
NASA Technical Reports Server (NTRS)
Kim, S.-W.
1991-01-01
A Navier-Stokes equations solver based on a pressure correction method with a pressure-staggered mesh and calculations of separated three-dimensional flows are presented. It is shown that the velocity pressure decoupling, which occurs when various pressure correction algorithms are used for pressure-staggered meshes, is caused by the ill-conditioned discrete pressure correction equation. The use of a partial differential equation for the incremental pressure eliminates the velocity pressure decoupling mechanism by itself and yields accurate numerical results. Example flows considered are a three-dimensional lid driven cavity flow and a laminar flow through a 90 degree bend square duct. For the lid driven cavity flow, the present numerical results compare more favorably with the measured data than those obtained using a formally third order accurate quadratic upwind interpolation scheme. For the curved duct flow, the present numerical method yields a grid independent solution with a very small number of grid points. The calculated velocity profiles are in good agreement with the measured data.
Ocular surface temperature: a 3D FEM prediction using bioheat equation.
Ng, E Y K; Ooi, E H
2007-06-01
Computational and mathematical human eye models from previous studies which were constructed in two-dimensions (2D) did not give a precise representation of the actual human eye. This work is an extension from an earlier published work on the 2D model. In this paper, a 3D FEM model of the human eye is simulated for the steady state temperature distribution during normal condition and during electromagnetic (EM) wave radiation. Results show a discrepancy of 0.49% for a normal condition as opposed to 1.9% of a 2D model when compared to experimental results from open literatures. Investigations on the EM wave radiations found an average power absorption density of 15,151 and 22,145 Wm(-3) for the 750 and 1500 MHz radiation, respectively. A peak temperature of 38.18( composite function)C was predicted for the 750 MHz radiation while 41.19( composite function)C was computed for the 1500 MHz radiation. These temperatures are in reasonable agreement with the simulated results computed by another report in the past. PMID:17034781
NASA Astrophysics Data System (ADS)
Chevalier, Paul; Bouchon, Patrick; Haïdar, Riad; Pardo, Fabrice
2014-08-01
Helmholtz resonators are widely used acoustic components able to select a single frequency. Here, based on an analogy between acoustics and electromagnetism wave equations, we present an electromagnetic 2D Helmholtz resonator made of a metallic slit-box structure. At the resonance, the light is funneled in the λ/800 apertures, and is subsequently absorbed in the cavity. As in acoustics, there is no higher order of resonance, which is an appealing feature for applications such as photodetection or thermal emission. Eventually, we demonstrate that the slit is of capacitive nature while the box behaves inductively. We derive an analytical formula for the resonance wavelength, which does not rely on wave propagation and therefore does not depend on the permittivity of the material filling the box. Besides, in contrast with half-wavelength resonators, the resonance wavelength can be engineered by both the slit aspect ratio and the box area.
Ott, C D; Dimmelmeier, H; Marek, A; Janka, H-T; Hawke, I; Zink, B; Schnetter, E
2007-06-29
We present 2D and 3D simulations of the collapse of rotating stellar iron cores in general relativity employing a nuclear equation of state and an approximate treatment of deleptonization. We compare fully general relativistic and conformally flat evolutions and find that the latter treatment is sufficiently accurate for the core-collapse supernova problem. We focus on gravitational wave (GW) emission from rotating collapse, bounce, and early postbounce phases. Our results indicate that the GW signature of these phases is much more generic than previously estimated. We also track the growth of a nonaxisymmetric instability in one model, leading to strong narrow-band GW emission. PMID:17678077
NASA Astrophysics Data System (ADS)
Green, A.; Gribenko, A.; Cuma, M.; Zhdanov, M. S.
2008-12-01
In this paper we apply 3D inversion to MT data collected in Oregon as a part of the EarthScope project. We use the integral equation method as a forward modeling engine. Quasi-analytical approximation with a variable background (QAVB) method of Frechet derivative calculation is applied. This technique allows us to simplify the inversion algorithm and to use just one forward modeling on every iteration step. The receiver footprint approach considerably reduces the computational resources needed to invert the large volumes of data covering vast areas. The data set, which was used in the inversion, was obtained through the Incorporated Research Institutions for Seismology (IRIS). The long-period MT data was collected in Eastern Oregon in 2006. The inverted electrical conductivity distribution agrees reasonably well with geological features of the region as well as with 3D MT inversion results obtained by other researchers. The geoelectrical model of the Oregon deep interior produced by 3D inversion indicates several lithospheres' electrical conductivity anomalies, including a linear zone marked by low-high conductivity transition along the Klamath Blue Mountain Lineament associated with a linear trend of gravity minima. High electrical conductivity values occur in the upper crust under the accreted terrains in the Blue Mountains region.
Local existence and Gevrey regularity of 3-D Navier-Stokes equations with ℓp initial data
NASA Astrophysics Data System (ADS)
Biswas, Animikh
We obtain local existence and Gevrey regularity of 3-D periodic Navier-Stokes equations in case the sequence of Fourier coefficients of the initial data is in ℓp (p<3/2). The ℓp norm of the sequence of Fourier coefficients of the solution and its analogous Gevrey norm remains bounded on a time interval whose length depends only on the size of the body force and the ℓp norm of the Fourier coefficient sequence of the initial data. The control on the Gevrey norm produces explicit estimates on the analyticity radius of the solution as in Foias and Temam (J. Funct. Anal. 87 (1989) 359-369). The results provide an alternate approach in estimating the space-analyticity radius of solutions to Navier-Stokes equations than the one presented by Grujić and Kukavica (J. Funct. Anal. 152 (1998) 447-466).
Recent advances in Runge-Kutta schemes for solving 3-D Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Vatsa, Veer N.; Wedan, Bruce W.; Abid, Ridha
1989-01-01
A thin-layer Navier-Stokes has been developed for solving high Reynolds number, turbulent flows past aircraft components under transonic flow conditions. The computer code has been validated through data comparisons for flow past isolated wings, wing-body configurations, prolate spheroids and wings mounted inside wind-tunnels. The basic code employs an explicit Runge-Kutta time-stepping scheme to obtain steady state solution to the unsteady governing equations. Significant gain in the efficiency of the code has been obtained by implementing a multigrid acceleration technique to achieve steady-state solutions. The improved efficiency of the code has made it feasible to conduct grid-refinement and turbulence model studies in a reasonable amount of computer time. The non-equilibrium turbulence model of Johnson and King has been extended to three-dimensional flows and excellent agreement with pressure data has been obtained for transonic separated flow over a transport type of wing.
Implicit scheme for Maxwell equations solution in case of flat 3D domains
NASA Astrophysics Data System (ADS)
Boronina, Marina; Vshivkov, Vitaly
2016-02-01
We present a new finite-difference scheme for Maxwell's equations solution for three-dimensional domains with different scales in different directions. The stability condition of the standard leap-frog scheme requires decreasing of the time-step with decreasing of the minimal spatial step, which depends on the minimal domain size. We overcome the conditional stability by modifying the standard scheme adding implicitness in the direction of the smallest size. The new scheme satisfies the Gauss law for the electric and magnetic fields in the final- differences. The approximation order, the maintenance of the wave amplitude and propagation speed, the invariance of the wave propagation on angle with the coordinate axes are analyzed.
Statistical shape analysis using 3D Poisson equation-A quantitatively validated approach.
Gao, Yi; Bouix, Sylvain
2016-05-01
Statistical shape analysis has been an important area of research with applications in biology, anatomy, neuroscience, agriculture, paleontology, etc. Unfortunately, the proposed methods are rarely quantitatively evaluated, and as shown in recent studies, when they are evaluated, significant discrepancies exist in their outputs. In this work, we concentrate on the problem of finding the consistent location of deformation between two population of shapes. We propose a new shape analysis algorithm along with a framework to perform a quantitative evaluation of its performance. Specifically, the algorithm constructs a Signed Poisson Map (SPoM) by solving two Poisson equations on the volumetric shapes of arbitrary topology, and statistical analysis is then carried out on the SPoMs. The method is quantitatively evaluated on synthetic shapes and applied on real shape data sets in brain structures. PMID:26874288
On the Helicity in 3D-Periodic Navier-Stokes Equations II: The Statistical Case
NASA Astrophysics Data System (ADS)
Foias, Ciprian; Hoang, Luan; Nicolaenko, Basil
2009-09-01
We study the asymptotic behavior of the statistical solutions to the Navier-Stokes equations using the normalization map [9]. It is then applied to the study of mean energy, mean dissipation rate of energy, and mean helicity of the spatial periodic flows driven by potential body forces. The statistical distribution of the asymptotic Beltrami flows are also investigated. We connect our mathematical analysis with the empirical theory of decaying turbulence. With appropriate mathematically defined ensemble averages, the Kolmogorov universal features are shown to be transient in time. We provide an estimate for the time interval in which those features may still be present. Our collaborator and friend Basil Nicolaenko passed away in September of 2007, after this work was completed. Honoring his contribution and friendship, we dedicate this article to him.
A Laplacian Equation Method for Numerical Generation of Boundary-Fitted 3D Orthogonal Grids
NASA Astrophysics Data System (ADS)
Theodoropoulos, T.; Bergeles, G. C.
1989-06-01
A sethod for generating boundary fitted orthogonal curvilinear grids in 3-dimensional space is described. The mapping between the curvilinear coordinates and the Cartesian coordinates is provided by a set of Laplace equations which, expressed in curvilinear coordinates, involve the components of the metric tensor and are therefore non-linear and coupled. An iterative algorithm is described, which achieves a numerical solution. Grids appropriate for the calculation of flow fields over complex topography or in complex flow passages as those found in turbomachinery, and for other engineering applications can be constructed using the proposed method. Various examples are presented and plotted in perspective, and data for the assessment of the properties of the resulting meshes is provided.
Calculation of a simulated 3-D high speed inlet using the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Knight, D. D.
1983-01-01
A hybrid numerical algorithm, developed to solve the full three-dimensional Navier-Stokes equations, is applied to the computation of the flowfield in a simulated three-dimensional high speed aircraft inlet at a Mach number of 2.5 and Reynolds number of 1.4 x 10 to the 7th based on inlet length. The numerical algorithm incorporates a coordinate transformation in order to handle general flow geometries, and utilizes the algebraic turbulent eddy viscosity model of Baldwin and Lomax. The hybrid algorithm has been vectorized on the CDC CYBER 203 computer using the SL/1 vector programming language developed at NASA Langley. The computed results are compared with experimental measurements of the ramp and cowl static pressures, and boundary layer pitot profiles. The results are also compared with a previous two-dimensional Navier-Stokes computation of the same configuration. The agreement with the experimental data is generally good; however, additional improvements in turbulence modeling are needed.
NASA Astrophysics Data System (ADS)
Amore, Paolo; Boyd, John P.; Fernández, Francisco M.; Rösler, Boris
2016-05-01
We apply second order finite differences to calculate the lowest eigenvalues of the Helmholtz equation, for complicated non-tensor domains in the plane, using different grids which sample exactly the border of the domain. We show that the results obtained applying Richardson and Padé-Richardson extrapolations to a set of finite difference eigenvalues corresponding to different grids allow us to obtain extremely precise values. When possible we have assessed the precision of our extrapolations comparing them with the highly precise results obtained using the method of particular solutions. Our empirical findings suggest an asymptotic nature of the FD series. In all the cases studied, we are able to report numerical results which are more precise than those available in the literature.
NASA Astrophysics Data System (ADS)
Pankratov, Oleg; Kuvshinov, Alexey
2016-01-01
second part, we summarize modern trends in the development of efficient 3-D EM forward modelling schemes with special emphasis on recent advances in the integral equation approach.
NASA Astrophysics Data System (ADS)
Shi, Jian; Zhang, Qian
2016-03-01
A uniqueness result of weak solution for the 3D viscous magneto-hydrodynamics equations in {B^1_{infty,infty}} is proved by means of the Fourier localization technique and the losing derivative estimates.
NASA Astrophysics Data System (ADS)
Ge, Liang; Sotiropoulos, Fotis
2007-08-01
A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow
NASA Technical Reports Server (NTRS)
Demuren, A. O.; Ibraheem, S. O.
1993-01-01
The convergence characteristics of various approximate factorizations for the 3D Euler and Navier-Stokes equations are examined using the von-Neumann stability analysis method. Three upwind-difference based factorizations and several central-difference based factorizations are considered for the Euler equations. In the upwind factorizations both the flux-vector splitting methods of Steger and Warming and van Leer are considered. Analysis of the Navier-Stokes equations is performed only on the Beam and Warming central-difference scheme. The range of CFL numbers over which each factorization is stable is presented for one-, two-, and three-dimensional flow. Also presented for each factorization is the CFL number at which the maximum eigenvalue is minimized, for all Fourier components, as well as for the high frequency range only. The latter is useful for predicting the effectiveness of multigrid procedures with these schemes as smoothers. Further, local mode analysis is performed to test the suitability of using a uniform flow field in the stability analysis. Some inconsistencies in the results from previous analyses are resolved.
NASA Astrophysics Data System (ADS)
Newton, W. G.; Stone, J. R.; Mezzacappa, A.
2006-09-01
First results from a fully self-consistent, temperature-dependent equation of state that spans the density range of neutron stars and supernova cores above neutron drip density are presented. The equation of state (EoS) is calculated using a mean-field Hartree-Fock method in three dimensions (3D). The nuclear interaction is represented by the phenomenological Skyrme model in this work, but the EoS can be obtained in our framework for any suitable form of the nucleon-nucleon effective interaction. The scheme we employ naturally allows effects such as (i) neutron drip, which results in an external neutron gas, (ii) the variety of exotic nuclear shapes expected for extremely neutron heavy nuclei, and (iii) the subsequent dissolution of these nuclei into nuclear matter. In this way, the equation of state is calculated across phase transitions without recourse to interpolation techniques between density regimes described by different physical models. EoS tables are calculated in the wide range of densities, temperature and proton/neutron ratios on the ORNL NCCS XT3, using up to 2000 processors simultaneously.
An IPOT meshless method using DC PSE approximation for fluid flow equations in 2D and 3D geometries
NASA Astrophysics Data System (ADS)
Bourantas, G. C.; Loukopoulos, V. C.; Skouras, E. D.; Burganos, V. N.; Nikiforidis, G. C.
2016-06-01
Navier-Stokes (N-S) equations, in their primitive variable (u-v-p) formulation, are numerically solved using the Implicit Potential (IPOT) numerical scheme in the context of strong form Meshless Point Collocation (MPC) method. The unknown field functions are computed using the Discretization Correction Particle Strength Exchange (DC PSE) approximation method. The latter makes use of discrete moment conditions to derive the operator kernels, which leads to low condition number for the moment matrix compared to other meshless interpolation methods and increased stability for the numerical solution. The proposed meshless scheme is applied on 2D and 3D spatial domains, using uniform or irregular set of nodes to represent the domain. The numerical results obtained are compared against those obtained using well-established methods.
NASA Astrophysics Data System (ADS)
Simpson, J. J.; Taflove, A.
2005-12-01
We report a finite-difference time-domain (FDTD) computational solution of Maxwell's equations [1] that models the possibility of detecting and characterizing ionospheric disturbances above seismic regions. Specifically, we study anomalies in Schumann resonance spectra in the extremely low frequency (ELF) range below 30 Hz as observed in Japan caused by a hypothetical cylindrical ionospheric disturbance above Taiwan. We consider excitation of the global Earth-ionosphere waveguide by lightning in three major thunderstorm regions of the world: Southeast Asia, South America (Amazon region), and Africa. Furthermore, we investigate varying geometries and characteristics of the ionospheric disturbance above Taiwan. The FDTD technique used in this study enables a direct, full-vector, three-dimensional (3-D) time-domain Maxwell's equations calculation of round-the-world ELF propagation accounting for arbitrary horizontal as well as vertical geometrical and electrical inhomogeneities and anisotropies of the excitation, ionosphere, lithosphere, and oceans. Our entire-Earth model grids the annular lithosphere-atmosphere volume within 100 km of sea level, and contains over 6,500,000 grid-points (63 km laterally between adjacent grid points, 5 km radial resolution). We use our recently developed spherical geodesic gridding technique having a spatial discretization best described as resembling the surface of a soccer ball [2]. The grid is comprised entirely of hexagonal cells except for a small fixed number of pentagonal cells needed for completion. Grid-cell areas and locations are optimized to yield a smoothly varying area difference between adjacent cells, thereby maximizing numerical convergence. We compare our calculated results with measured data prior to the Chi-Chi earthquake in Taiwan as reported by Hayakawa et. al. [3]. Acknowledgement This work was suggested by Dr. Masashi Hayakawa, University of Electro-Communications, Chofugaoka, Chofu Tokyo. References [1] A
On the Finite-Time Splash and Splat Singularities for the 3-D Free-Surface Euler Equations
NASA Astrophysics Data System (ADS)
Coutand, Daniel; Shkoller, Steve
2014-01-01
We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in Castro et al. (Splash singularity for water waves, http://arxiv.org/abs/1106.2120v2, 2011), wherein the evolving 2-D hypersurface, the moving boundary of the fluid domain, self-intersects at a point (or on surface). Such singularities can occur when the crest of a breaking wave falls unto its trough, or in the study of drop impact upon liquid surfaces. Our approach is founded upon the Lagrangian description of the free-boundary problem, combined with a novel approximation scheme of a finite collection of local coordinate charts; as such we are able to analyze a rather general set of geometries for the evolving 2-D free-surface of the fluid. We do not assume the fluid is irrotational, and as such, our method can be used for a number of other fluid interface problems, including compressible flows, plasmas, as well as the inclusion of surface tension effects.
NASA Astrophysics Data System (ADS)
Gainullin, I. K.; Sonkin, M. A.
2015-03-01
A parallelized three-dimensional (3D) time-dependent Schrodinger equation (TDSE) solver for one-electron systems is presented in this paper. The TDSE Solver is based on the finite-difference method (FDM) in Cartesian coordinates and uses a simple and explicit leap-frog numerical scheme. The simplicity of the numerical method provides very efficient parallelization and high performance of calculations using Graphics Processing Units (GPUs). For example, calculation of 106 time-steps on the 1000ṡ1000ṡ1000 numerical grid (109 points) takes only 16 hours on 16 Tesla M2090 GPUs. The TDSE Solver demonstrates scalability (parallel efficiency) close to 100% with some limitations on the problem size. The TDSE Solver is validated by calculation of energy eigenstates of the hydrogen atom (13.55 eV) and affinity level of H- ion (0.75 eV). The comparison with other TDSE solvers shows that a GPU-based TDSE Solver is 3 times faster for the problems of the same size and with the same cost of computational resources. The usage of a non-regular Cartesian grid or problem-specific non-Cartesian coordinates increases this benefit up to 10 times. The TDSE Solver was applied to the calculation of the resonant charge transfer (RCT) in nanosystems, including several related physical problems, such as electron capture during H+-H0 collision and electron tunneling between H- ion and thin metallic island film.
NASA Astrophysics Data System (ADS)
Zhai, Cuili; Zhang, Ting
2015-09-01
In this article, we consider the global well-posedness to the 3-D incompressible inhomogeneous Navier-Stokes equations with a class of large velocity. More precisely, assuming a 0 ∈ B˙ q , 1 /3 q ( R 3 ) and u 0 = ( u0 h , u0 3 ) ∈ B˙ p , 1 - 1 + /3 p ( R 3 ) for p, q ∈ (1, 6) with sup ( /1 p , /1 q ) ≤ /1 3 + inf ( /1 p , /1 q ) , we prove that if C a↑0↑ B˙q1/3 q α (↑u0 3↑ B˙ p , 1 - 1 + /3 p/μ + 1 ) ≤ 1 , /C μ (↑u0 h↑ B˙ p , 1 - 1 + /3 p + ↑u03↑ B˙ p , 1 - 1 + /3 p 1 - α ↑u0h↑ B˙ p , 1 - 1 + /3 p α) ≤ 1 , then the system has a unique global solution a ∈ C ˜ ( [ 0 , ∞ ) ; B˙ q , 1 /3 q ( R 3 ) ) , u ∈ C ˜ ( [ 0 , ∞ ) ; B˙ p , 1 - 1 + /3 p ( R 3 ) ) ∩ L 1 ( R + ; B˙ p , 1 1 + /3 p ( R 3 ) ) . It improves the recent result of M. Paicu and P. Zhang [J. Funct. Anal. 262, 3556-3584 (2012)], where the exponent form of the initial smallness condition is replaced by a polynomial form.
ERIC Educational Resources Information Center
Merchant, Zahira; Goetz, Ernest T.; Keeney-Kennicutt, Wendy; Kwok, Oi-man; Cifuentes, Lauren; Davis, Trina J.
2012-01-01
We examined a model of the impact of a 3D desktop virtual reality environment on the learner characteristics (i.e. perceptual and psychological variables) that can enhance chemistry-related learning achievements in an introductory college chemistry class. The relationships between the 3D virtual reality features and the chemistry learning test as…
NASA Technical Reports Server (NTRS)
Abdol-Hamid, Khaled S.
1990-01-01
The development and applications of multiblock/multizone and adaptive grid methodologies for solving the three-dimensional simplified Navier-Stokes equations are described. Adaptive grid and multiblock/multizone approaches are introduced and applied to external and internal flow problems. These new implementations increase the capabilities and flexibility of the PAB3D code in solving flow problems associated with complex geometry.
Dahms, Rainer N.
2014-12-31
The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phase components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. As a result, the new model preserves the accuracy of previous
Dahms, Rainer N.
2014-12-31
The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phasemore » components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. As a result, the new model preserves the accuracy of
NASA Astrophysics Data System (ADS)
Bustamante, Miguel D.
2014-11-01
We consider 3D Euler fluids endowed with a discrete symmetry whereby the velocity field is invariant under mirror reflections about a 2D surface known as the ``symmetry plane.'' This type of flow is widely used in numerical simulations of classical/magnetic/quantum turbulence and vortex reconnection. On the 2D symmetry plane, the governing equations are best written in terms of two scalars: vorticity and stretching rate of vorticity. These determine the velocity field on the symmetry plane. However, the governing equations are not closed, because of the contribution of a single pressure term that depends on the full 3D velocity profile. By modelling this pressure term we propose a one-parameter family of sensible models for the flow along the 2D symmetry plane. We apply the method of infinitesimal Lie symmetries and solve the governing equations analytically for the two scalars as functions of time. We show how the value of the model's parameter determines if the analytical solution has a finite-time blowup and obtain explicit formulae for the blowup time. We validate the models by showing that a particular choice of the model's parameter corresponds to a well-known exact solution of 3D Euler equations [Gibbon et al., Physica D 132, 497 (1999)]. We discuss practical applications. Supported by Science Foundation Ireland (SFI) under Grant Number 12/IP/1491.
NASA Technical Reports Server (NTRS)
Kwak, D.
1994-01-01
INS3D computes steady-state solutions to the incompressible Navier-Stokes equations. The INS3D approach utilizes pseudo-compressibility combined with an approximate factorization scheme. This computational fluid dynamics (CFD) code has been verified on problems such as flow through a channel, flow over a backwardfacing step and flow over a circular cylinder. Three dimensional cases include flow over an ogive cylinder, flow through a rectangular duct, wind tunnel inlet flow, cylinder-wall juncture flow and flow through multiple posts mounted between two plates. INS3D uses a pseudo-compressibility approach in which a time derivative of pressure is added to the continuity equation, which together with the momentum equations form a set of four equations with pressure and velocity as the dependent variables. The equations' coordinates are transformed for general three dimensional applications. The equations are advanced in time by the implicit, non-iterative, approximately-factored, finite-difference scheme of Beam and Warming. The numerical stability of the scheme depends on the use of higher-order smoothing terms to damp out higher-frequency oscillations caused by second-order central differencing. The artificial compressibility introduces pressure (sound) waves of finite speed (whereas the speed of sound would be infinite in an incompressible fluid). As the solution converges, these pressure waves die out, causing the derivation of pressure with respect to time to approach zero. Thus, continuity is satisfied for the incompressible fluid in the steady state. Computational efficiency is achieved using a diagonal algorithm. A block tri-diagonal option is also available. When a steady-state solution is reached, the modified continuity equation will satisfy the divergence-free velocity field condition. INS3D is capable of handling several different types of boundaries encountered in numerical simulations, including solid-surface, inflow and outflow, and far
Kamon, M.; Phillips, J.R.
1994-12-31
In this paper techniques are presented for preconditioning equations generated by discretizing constrained vector integral equations associated with magnetoquasistatic analysis. Standard preconditioning approaches often fail on these problems. The authors present a specialized preconditioning technique and prove convergence bounds independent of the constraint equations and electromagnetic excitation frequency. Computational results from analyzing several electronic packaging examples are given to demonstrate that the new preconditioning approach can sometimes reduce the number of GMRES iterations by more than an order of magnitude.
2013 Problem 12: Helmholtz Carousel
NASA Astrophysics Data System (ADS)
Qi, Jia'an; Qin, Zhihang; Wang, Sihui; Zhou, Huijun
2015-10-01
In our solution, we try to investigate the origin of the force that propels the Helmholtz Carousel. We build a theoretical model from the fundamental hydrodynamics. As the propelling force is in fact a nonlinear effect, we examine the nonlinear terms with care. The nonlinear terms in our equation corresponding to two origins of the force: one origins from the nonlinearity of the impedance, the other origins from nonlinear "restoring force". We will prove that the true origin of the force effect is the nonlinear impedance, which resembles the recoil force of a balloon that breathes air in and out unsymmetrically in a period of motion. Modification to linear impedance is also made which is important in giving a correct resonant frequency. Finally, we optimize the Helmholtz carousel according to the predictions of our model. Among the parameters we investigated, specific frequency, neck length, neck radius values exist to optimize the Helmholtz carousel, while larger resonator volume produces larger driving force. Predictions based on our model are supported by experimental results.
NASA Astrophysics Data System (ADS)
Vidal, A.; San-Blas, A. A.; Quesada-Pereira, F. D.; Pérez-Soler, J.; Gil, J.; Vicente, C.; Gimeno, B.; Boria, V. E.
2015-07-01
A novel technique for the full-wave analysis of 3-D complex waveguide devices is presented. This new formulation, based on the Boundary Integral-Resonant Mode Expansion (BI-RME) method, allows the rigorous full-wave electromagnetic characterization of 3-D arbitrarily shaped metallic structures making use of extremely low CPU resources (both time and memory). The unknown electric current density on the surface of the metallic elements is represented by means of Rao-Wilton-Glisson basis functions, and an algebraic procedure based on a singular value decomposition is applied to transform such functions into the classical solenoidal and nonsolenoidal basis functions needed by the original BI-RME technique. The developed tool also provides an accurate computation of the electromagnetic fields at an arbitrary observation point of the considered device, so it can be used for predicting high-power breakdown phenomena. In order to validate the accuracy and efficiency of this novel approach, several new designs of band-pass waveguides filters are presented. The obtained results (S-parameters and electromagnetic fields) are successfully compared both to experimental data and to numerical simulations provided by a commercial software based on the finite element technique. The results obtained show that the new technique is specially suitable for the efficient full-wave analysis of complex waveguide devices considering an integrated coaxial excitation, where the coaxial probes may be in contact with the metallic insets of the component.
On Bi-Grid Local Mode Analysis of Solution Techniques for 3-D Euler and Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Ibraheem, S. O.; Demuren, A. O.
1994-01-01
A procedure is presented for utilizing a bi-grid stability analysis as a practical tool for predicting multigrid performance in a range of numerical methods for solving Euler and Navier-Stokes equations. Model problems based on the convection, diffusion and Burger's equation are used to illustrate the superiority of the bi-grid analysis as a predictive tool for multigrid performance in comparison to the smoothing factor derived from conventional von Neumann analysis. For the Euler equations, bi-grid analysis is presented for three upwind difference based factorizations, namely Spatial, Eigenvalue and Combination splits, and two central difference based factorizations, namely LU and ADI methods. In the former, both the Steger-Warming and van Leer flux-vector splitting methods are considered. For the Navier-Stokes equations, only the Beam-Warming (ADI) central difference scheme is considered. In each case, estimates of multigrid convergence rates from the bi-grid analysis are compared to smoothing factors obtained from single-grid stability analysis. Effects of grid aspect ratio and flow skewness are examined. Both predictions are compared with practical multigrid convergence rates for 2-D Euler and Navier-Stokes solutions based on the Beam-Warming central scheme.
Holography, tomography and 3D microscopy as linear filtering operations
NASA Astrophysics Data System (ADS)
Coupland, J. M.; Lobera, J.
2008-07-01
In this paper, we characterize 3D optical imaging techniques as 3D linear shift-invariant filtering operations. From the Helmholtz equation that is the basis of scalar diffraction theory, we show that the scattered field, or indeed a holographic reconstruction of this field, can be considered to be the result of a linear filtering operation applied to a source distribution. We note that if the scattering is weak, the source distribution is independent of the scattered field and a holographic reconstruction (or in fact any far-field optical imaging system) behaves as a 3D linear shift-invariant filter applied to the refractive index contrast (which effectively defines the object). We go on to consider tomographic techniques that synthesize images from recordings of the scattered field using different illumination conditions. In our analysis, we compare the 3D response of monochromatic optical tomography with the 3D imagery offered by confocal microscopy and scanning white light interferometry (using quasi-monochromatic illumination) and explain the circumstances under which these approaches are equivalent. Finally, we consider the 3D response of polychromatic optical tomography and in particular the response of spectral optical coherence tomography and scanning white light interferometry.
NASA Astrophysics Data System (ADS)
Young, D. L.; Tsai, C. H.; Wu, C. S.
2015-11-01
An alternative vector potential formulation is used to solve the Navier-Stokes (N-S) equations in 3D incompressible viscous flow problems with and without through-flow boundaries. Difficulties of the vector potential formulation include the implementation of boundary conditions for through-flow boundaries and the numerical treatment of fourth-order partial differential equations. The advantages on the other hand are the automatic satisfaction of the continuity equation; and pressure is decoupled from the velocity. The objective of this paper is to introduce the appropriate gauge and boundary conditions on the vector potential formulation by a localized meshless method. To handle the divergence-free property, a Coulomb gauge condition is enforced on the vector potential to ensure its existence and uniqueness mathematically. We further improve the algorithm to through-flow problems for the boundary conditions of vector potential by introducing the concept of Stokes' theorem. Based on this innovation, there is no need to include an additional variable to tackle the through-flow fields. This process will greatly simplify the imposition of boundary conditions by the vector potential approach. Under certain conditions, the coupled fourth-order partial differential equations can be easily solved by using this meshless local differential quadrature (LDQ) method. Due to the LDQ capability to deal with the high order differential equations, this algorithm is very attractive to solve this fourth-order vector potential formulation for the N-S equations as comparing to the conventional numerical schemes such as finite element or finite difference methods. The proposed vector potential formulation is simpler and has improved accuracy and efficiency compared to other pressure-free or pressure-coupled algorithms. This investigation can be regarded as the first complete study to obtain the N-S solutions by vector potential formulation through a LDQ method. Two classic 3D benchmark
On the Rigorous Derivation of the 3D Cubic Nonlinear Schrödinger Equation with a Quadratic Trap
NASA Astrophysics Data System (ADS)
Chen, Xuwen
2013-11-01
We consider the dynamics of the three-dimensional N-body Schrödinger equation in the presence of a quadratic trap. We assume the pair interaction potential is N 3 β-1 V( N β x). We justify the mean-field approximation and offer a rigorous derivation of the three-dimensional cubic nonlinear Schrödinger equation (NLS) with a quadratic trap. We establish the space-time bound conjectured by Klainerman and Machedon (Commun Math Phys 279:169-185, 2008) for by adapting and simplifying an argument in Chen and Pavlović (Annales Henri Poincaré, 2013) which solves the problem for in the absence of a trap.
NASA Astrophysics Data System (ADS)
Yuasa, T.; Sunaguchi, N.; Ichihara, S.; Ando, M.
2013-05-01
Refraction-contrast computed tomography (CT) can image biological soft tissues and soft materials at a high contrast, which cannot be clearly depicted by contemporary CT based on absorption contrast. It reconstructs a distribution of refractive index from projections, whose data each is an angular deviation from incident direction due to refraction by an object, and is acquired by imaging methods using an angular analyzer, e.g., DEI (diffraction enhance imaging), or DFI (dark field imaging). First, a reconstruction algorithm for refraction-contrast CT is derived from the ray equation of a fundamental equation describing refraction phenomena in geometrical optics. Then, in order to demonstrate its efficacy, we performed imaging experiment using DFI-CT imaging system. A reconstructed image of human breast cancer tissue is presented.
Meng, Da; Zheng, Bin; Lin, Guang; Sushko, Maria L.
2014-08-29
We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is the number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.
NASA Astrophysics Data System (ADS)
Tsuzuki, Yutaka
2015-09-01
This paper is concerned with a system of heat equations with hysteresis and Navier-Stokes equations. In Tsuzuki (J Math Anal Appl 423:877-897, 2015) an existence result is obtained for the problem in a 2-dimensional domain with the Navier-Stokes equation in a weak sense. However the result does not include uniqueness for the problem due to the low regularity for solutions. This paper establishes existence and uniqueness in 2- and 3-dimensional domains with the Navier-Stokes equation in a stronger sense. Moreover this work decides required height of regularity for the initial data by introducing the fractional power of the Stokes operator.
NASA Technical Reports Server (NTRS)
Zhang, Jun; Ge, Lixin; Kouatchou, Jules
2000-01-01
A new fourth order compact difference scheme for the three dimensional convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it Only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with the Gauss-Seidel type iterative method. This is compared with the known 19 point fourth order compact differenCe scheme which requires four colors to decouple the computational grid. Numerical results, with multigrid methods implemented on a shared memory parallel computer, are presented to compare the 15 point and the 19 point fourth order compact schemes.
NASA Astrophysics Data System (ADS)
DeJong, Andrew
Numerical models of fluid-structure interaction have grown in importance due to increasing interest in environmental energy harvesting, airfoil-gust interactions, and bio-inspired formation flying. Powered by increasingly powerful parallel computers, such models seek to explain the fundamental physics behind the complex, unsteady fluid-structure phenomena. To this end, a high-fidelity computational model based on the high-order spectral difference method on 3D unstructured, dynamic meshes has been developed. The spectral difference method constructs continuous solution fields within each element with a Riemann solver to compute the inviscid fluxes at the element interfaces and an averaging mechanism to compute the viscous fluxes. This method has shown promise in the past as a highly accurate, yet sufficiently fast method for solving unsteady viscous compressible flows. The solver is monolithically coupled to the equations of motion of an elastically mounted 3-degree of freedom rigid bluff body undergoing flow-induced lift, drag, and torque. The mesh is deformed using 4 methods: an analytic function, Laplace equation, biharmonic equation, and a bi-elliptic equation with variable diffusivity. This single system of equations -- fluid and structure -- is advanced through time using a 5-stage, 4th-order Runge-Kutta scheme. Message Passing Interface is used to run the coupled system in parallel on up to 240 processors. The solver is validated against previously published numerical and experimental data for an elastically mounted cylinder. The effect of adding an upstream body and inducing wake galloping is observed.
NASA Technical Reports Server (NTRS)
Cwik, T.; Jamnejad, V.; Zuffada, C.
1993-01-01
It is often desirable to calculate the electromagnetic fields inside and about a complicated system of scattering bodies, as well as in their far-field region. The finite element method (FE) is well suited to solving the interior problem, but the domain has to be limited to a manageable size. At the truncation of the FE mesh one can either impose approximate (absorbing) boundary conditions or set up an integral equation (IE) for the fields scattered from the bodies. The latter approach is preferable since it results in higher accuracy. Hence, the two techniques can be successfully combined by introducing a surface that encloses the scatterers, applying a FE model to the inner volume and setting up an IE for the tangential fields components on the surface. Here the continuity of the tangential fields is used bo obtain a consistent solution. A few coupled FE-IE methods have recently appeared in the literature. The approach presented here has the advantage of using edge-based finite elements, a type of finite elements with degrees of freedom associated with edges of the mesh. Because of their properties, they are better suited than the conventional node based elements to represent electromagnetic fields, particularly when inhomogeneous regions are modeled, since the node based elements impose an unnatural continuity of all field components across boundaries of mesh elements. Additionally, our approach is well suited to handle large size problems and lends itself to code parallelization. We will discuss the salient features that make our approach very efficient from the standpoint of numerical computation, and the fields and RCS of a few objects are illustrated as examples.
Joukar, Amin; Nammakie, Erfan; Niroomand-Oscuii, Hanieh
2015-01-01
The application of laser in ophthalmology and eye surgery is so widespread that hardly can anyone deny its importance. On the other hand, since the human eye is an organ susceptible to external factors such as heat waves, laser radiation rapidly increases the temperature of the eye and therefore the study of temperature distribution inside the eye under laser irradiation is crucial; but the use of experimental and invasive methods for measuring the temperature inside the eye is typically high-risk and hazardous. In this paper, using the three-dimensional finite element method, the distribution of heat transfer inside the eye under transient condition was studied through three different lasers named Nd:Yag, Nd:Yap and ArF. Considering the metabolic heat and blood perfusion rate in various regions of the eye, numerical solution of space-time dependant Pennes bioheat transfer equation has been applied in this study. Lambert-Beer's law has been used to model the absorption of laser energy inside the eye tissues. It should also be mentioned that the effect of the ambient temperature, tear evaporation rate, laser power and the pupil diameter on the temperature distribution have been studied. Also, temperature distribution inside the eye after applying each laser and temperature variations of six optional regions as functions of time have been investigated. The results show that these radiations cause temperature rise in various regions, which will in turn causes serious damages to the eye tissues. Investigating the temperature distribution inside the eye under the laser irradiation can be a useful tool to study and predict the thermal effects of laser radiation on the human eye and evaluate the risk involved in performing laser surgery. PMID:25774029
Blumberg, L.N.
1992-03-01
The authors have analyzed simulated magnetic measurements data for the SXLS bending magnet in a plane perpendicular to the reference axis at the magnet midpoint by fitting the data to an expansion solution of the 3-dimensional Laplace equation in curvilinear coordinates as proposed by Brown and Servranckx. The method of least squares is used to evaluate the expansion coefficients and their uncertainties, and compared to results from an FFT fit of 128 simulated data points on a 12-mm radius circle about the reference axis. They find that the FFT method gives smaller coefficient uncertainties that the Least Squares method when the data are within similar areas. The Least Squares method compares more favorably when a larger number of data points are used within a rectangular area of 30-mm vertical by 60-mm horizontal--perhaps the largest area within the 35-mm x 75-mm vacuum chamber for which data could be obtained. For a grid with 0.5-mm spacing within the 30 x 60 mm area the Least Squares fit gives much smaller uncertainties than the FFT. They are therefore in the favorable position of having two methods which can determine the multipole coefficients to much better accuracy than the tolerances specified to General Dynamics. The FFT method may be preferable since it requires only one Hall probe rather than the four envisioned for the least squares grid data. However least squares can attain better accuracy with fewer probe movements. The time factor in acquiring the data will likely be the determining factor in choice of method. They should further explore least squares analysis of a Fourier expansion of data on a circle or arc of a circle since that method gives coefficient uncertainties without need for multiple independent sets of data as needed by the FFT method.
NASA Astrophysics Data System (ADS)
Porter, K.
2015-12-01
There are two common ways to create a ground-motion map for a hypothetical earthquake: using ground motion prediction equations (by far the more common of the two) and using 3-D physics-based modeling. The former is very familiar to engineers, the latter much less so, and the difference can present a problem because engineers tend to trust the familiar and distrust novelty. Maps for essentially the same hypothetical earthquake using the two different methods can look very different, while appearing to present the same information. Using one or the other can lead an engineer or disaster planner to very different estimates of damage and risk. The reasons have to do with depiction of variability, spatial correlation of shaking, the skewed distribution of real-world shaking, and the upward-curving relationship between shaking and damage. The scientists who develop the two kinds of map tend to specialize in one or the other and seem to defend their turf, which can aggravate the problem of clearly communicating with engineers.The USGS Science Application for Risk Reduction's (SAFRR) HayWired scenario has addressed the challenge of explaining to engineers the differences between the two maps, and why, in a disaster planning scenario, one might want to use the less-familiar 3-D map.
NASA Astrophysics Data System (ADS)
Li, Liang; Lanteri, Stéphane; Perrussel, Ronan
2014-01-01
A Schwarz-type domain decomposition method is presented for the solution of the system of 3d time-harmonic Maxwell's equations. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of the problem based on a tetrahedrization of the computational domain. The discrete system of the HDG method on each subdomain is solved by an optimized sparse direct (LU factorization) solver. The solution of the interface system in the domain decomposition framework is accelerated by a Krylov subspace method. The formulation and the implementation of the resulting DD-HDG (Domain Decomposed-Hybridizable Discontinuous Galerkin) method are detailed. Numerical results show that the resulting DD-HDG solution strategy has an optimal convergence rate and can save both CPU time and memory cost compared to a classical upwind flux-based DD-DG (Domain Decomposed-Discontinuous Galerkin) approach.
NASA Astrophysics Data System (ADS)
Gerke, Kirill; Vasilyev, Roman; Khirevich, Siarhei; Karsanina, Marina; Collins, Daniel; Korost, Dmitry; Mallants, Dirk
2015-04-01
In this contribution we introduce a novel free software which solves the Stokes equation to obtain velocity fields for low Reynolds-number flows within externally generated 3D pore geometries. Provided with velocity fields, one can calculate permeability for known pressure gradient boundary conditions via Darcy's equation. Finite-difference schemes of 2nd and 4th order of accuracy are used together with an artificial compressibility method to iteratively converge to a steady-state solution of Stokes' equation. This numerical approach is much faster and less computationally demanding than the majority of open-source or commercial softwares employing other algorithms (finite elements/volumes, lattice Boltzmann, etc.) The software consists of two parts: 1) a pre and post-processing graphical interface, and 2) a solver. The latter is efficiently parallelized to use any number of available cores (the speedup on 16 threads was up to 10-12 depending on hardware). Due to parallelization and memory optimization our software can be used to obtain solutions for 300x300x300 voxels geometries on modern desktop PCs. The software was successfully verified by testing it against lattice Boltzmann simulations and analytical solutions. To illustrate the software's applicability for numerous problems in Earth Sciences, a number of case studies have been developed: 1) identifying the representative elementary volume for permeability determination within a sandstone sample, 2) derivation of permeability/hydraulic conductivity values for rock and soil samples and comparing those with experimentally obtained values, 3) revealing the influence of the amount of fine-textured material such as clay on filtration properties of sandy soil. This work was partially supported by RSF grant 14-17-00658 (pore-scale modelling) and RFBR grants 13-04-00409-a and 13-05-01176-a.
3-D FDTD simulation of shear waves for evaluation of complex modulus imaging.
Orescanin, Marko; Wang, Yue; Insana, Michael
2011-02-01
The Navier equation describing shear wave propagation in 3-D viscoelastic media is solved numerically with a finite differences time domain (FDTD) method. Solutions are formed in terms of transverse scatterer velocity waves and then verified via comparison to measured wave fields in heterogeneous hydrogel phantoms. The numerical algorithm is used as a tool to study the effects on complex shear modulus estimation from wave propagation in heterogeneous viscoelastic media. We used an algebraic Helmholtz inversion (AHI) technique to solve for the complex shear modulus from simulated and experimental velocity data acquired in 2-D and 3-D. Although 3-D velocity estimates are required in general, there are object geometries for which 2-D inversions provide accurate estimations of the material properties. Through simulations and experiments, we explored artifacts generated in elastic and dynamic-viscous shear modulus images related to the shear wavelength and average viscosity. PMID:21342824
Ghosh, Aryya; Vaval, Nayana; Pal, Sourav
2015-07-14
Auger decay is an efficient ultrafast relaxation process of core-shell or inner-shell excited atom or molecule. Generally, it occurs in femto-second or even atto-second time domain. Direct measurement of lifetimes of Auger process of single ionized and double ionized inner-shell state of an atom or molecule is an extremely difficult task. In this paper, we have applied the highly correlated complex absorbing potential-equation-of-motion coupled cluster (CAP-EOMCC) approach which is a combination of CAP and EOMCC approach to calculate the lifetime of the states arising from 2p inner-shell ionization of an Ar atom and 3d inner-shell ionization of Kr atom. We have also calculated the lifetime of Ar{sup 2+}(2p{sup −1}3p{sup −1}) {sup 1}D, Ar{sup 2+}(2p{sup −1}3p{sup −1}) {sup 1}S, and Ar{sup 2+}(2p{sup −1}3s{sup −1}) {sup 1}P double ionized states. The predicted results are compared with the other theoretical results as well as experimental results available in the literature.
Nonlinearity of Helmholtz resonators
NASA Technical Reports Server (NTRS)
Sirignano, W. A.
1972-01-01
Consideration of the nonlinear damping of pressure oscillations by means of acoustic liners consisting of a perforated plate communicating with a volume or of individual Helmholtz resonators. A nonlinear analysis leads to a modified first-order theory; in particular, some second-order damping effects (due to the formation of jets through the orifices) are considered, while other less important damping effects (of second order) are neglected. The effect of the vena contracta in the orifice flow is also taken into account, and the conditions of maximum damping are discussed. A determination is made of the orifice velocity, the cavity pressure, the admittance coefficient, the resistance, and the reactance, and good agreement is found between the theoretically determined resistance and orifice velocity and the pertinent experimental data.
Generalized Helmholtz Conditions for Non-Conservative Lagrangian Systems
NASA Astrophysics Data System (ADS)
Bucataru, Ioan; Constantinescu, Oana
2015-12-01
In this paper we provide generalized Helmholtz conditions, in terms of a semi-basic 1-form, which characterize when a given system of second order ordinary differential equations is equivalent to the Lagrange equations, for some given arbitrary non-conservative forces. For the particular cases of dissipative or gyroscopic forces, these conditions, when expressed in terms of a multiplier matrix, reduce to those obtained in Mestdag et al. (Differential Geom. Appl. 29(1), 55-72, 2011). When the involved geometric structures are homogeneous with respect to the fibre coordinates, we show how one can further simplify the generalized Helmholtz conditions. We provide examples where the proposed generalized Helmholtz conditions, expressed in terms of a semi-basic 1-form, can be integrated and the corresponding Lagrangian and Lagrange equations can be found.
NASA Astrophysics Data System (ADS)
Wang, F.; Jordan, T. H.
2012-12-01
Seismic hazard models based on empirical ground motion prediction equations (GMPEs) employ a model-based factorization to account for source, propagation, and path effects. An alternative is to simulate these effects directly using earthquake source models combined with three-dimensional (3D) models of Earth structure. We have developed an averaging-based factorization (ABF) scheme that facilitates the geographically explicit comparison of these two types of seismic hazard models. For any fault source k with epicentral position x, slip spatial and temporal distribution f, and moment magnitude m, we calculate the excitation functions G(s, k, x, m, f) for sites s in a geographical region R, such as 5% damped spectral acceleration at a particular period. Through a sequence of weighted-averaging and normalization operations following a certain hierarchy over f, m, x, k, and s, we uniquely factorize G(s, k, x, m, f) into six components: A, B(s), C(s, k), D(s, k, x), E(s, k, x, m), and F(s, k, x, m, f). Factors for a target model can be divided by those of a reference model to obtain six corresponding factor ratios, or residual factors: a, b(s), c(s, k), d(s, k, x), e(s, k, x, m), and f(s, k, x, m, f). We show that these residual factors characterize differences in basin effects primarily through b(s), distance scaling primarily through c(s, k), and source directivity primarily through d(s, k, x). We illustrate the ABF scheme by comparing CyberShake Hazard Model (CSHM) for the Los Angeles region (Graves et. al. 2010) with the Next Generation Attenuation (NGA) GMPEs modified according to the directivity relations of Spudich and Chiou (2008). Relative to CSHM, all NGA models underestimate the directivity and basin effects. In particular, the NGA models do not account for the coupling between source directivity and basin excitation that substantially enhance the low-frequency seismic hazards in the sedimentary basins of the Los Angeles region. Assuming Cyber
NASA Astrophysics Data System (ADS)
Pletinckx, D.
2011-09-01
The current 3D hype creates a lot of interest in 3D. People go to 3D movies, but are we ready to use 3D in our homes, in our offices, in our communication? Are we ready to deliver real 3D to a general public and use interactive 3D in a meaningful way to enjoy, learn, communicate? The CARARE project is realising this for the moment in the domain of monuments and archaeology, so that real 3D of archaeological sites and European monuments will be available to the general public by 2012. There are several aspects to this endeavour. First of all is the technical aspect of flawlessly delivering 3D content over all platforms and operating systems, without installing software. We have currently a working solution in PDF, but HTML5 will probably be the future. Secondly, there is still little knowledge on how to create 3D learning objects, 3D tourist information or 3D scholarly communication. We are still in a prototype phase when it comes to integrate 3D objects in physical or virtual museums. Nevertheless, Europeana has a tremendous potential as a multi-facetted virtual museum. Finally, 3D has a large potential to act as a hub of information, linking to related 2D imagery, texts, video, sound. We describe how to create such rich, explorable 3D objects that can be used intuitively by the generic Europeana user and what metadata is needed to support the semantic linking.
The Helmholtz Hierarchy: phase space statistics of cold dark matter
Tassev, Svetlin V.
2011-10-01
We present a new formalism to study large-scale structure in the universe. The result is a hierarchy (which we call the ''Helmholtz Hierarchy'') of equations describing the phase space statistics of cold dark matter (CDM). The hierarchy features a physical ordering parameter which interpolates between the Zel'dovich approximation and fully-fledged gravitational interactions. The results incorporate the effects of stream crossing. We show that the Helmholtz hierarchy is self-consistent and obeys causality to all orders. We present an interpretation of the hierarchy in terms of effective particle trajectories.
PLOT3D/AMES, APOLLO UNIX VERSION USING GMR3D (WITH TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
PLOT3D/AMES, APOLLO UNIX VERSION USING GMR3D (WITHOUT TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
NASA Astrophysics Data System (ADS)
Ren, Dandan; Ou, Yaobin
2016-08-01
In this paper, we prove the incompressible limit of all-time strong solutions to the three-dimensional full compressible Navier-Stokes equations. Here the velocity field and temperature satisfy the Dirichlet boundary condition and convective boundary condition, respectively. The uniform estimates in both the Mach number {ɛin(0,overline{ɛ}]} and time {tin[0,∞)} are established by deriving a differential inequality with decay property, where {overline{ɛ} in(0,1]} is a constant. Based on these uniform estimates, the global solution of full compressible Navier-Stokes equations with "well-prepared" initial conditions converges to the one of isentropic incompressible Navier-Stokes equations as the Mach number goes to zero.
NASA Technical Reports Server (NTRS)
Shareef, N. H.; Amirouche, F. M. L.
1991-01-01
A computational algorithmic procedure is developed and implemented for the dynamic analysis of a multibody system with rigid/flexible interconnected bodies. The algorithm takes into consideration the large rotation/translation and small elastic deformations associated with the rigid-body degrees of freedom and the flexibility of the bodies in the system respectively. Versatile three-dimensional isoparametric brick elements are employed for the modeling of the geometric configurations of the bodies. The formulation of the recursive dynamical equations of motion is based on the recursive Kane's equations, strain energy concepts, and the techniques of component mode synthesis. In order to minimize CPU-intensive matrix multiplication operations and speed up the execution process, the concepts of indexed arrays is utilized in the formulation of the equations of motion. A spin-up maneuver of a space robot with three flexible links carrying a solar panel is used as an illustrative example.
3d-3d correspondence revisited
NASA Astrophysics Data System (ADS)
Chung, Hee-Joong; Dimofte, Tudor; Gukov, Sergei; Sułkowski, Piotr
2016-04-01
In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d {N}=2 theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomials. Higgsing the full 3d theories constructed this way recovers theories found previously by Dimofte-Gaiotto-Gukov. We also consider the cutting and gluing of 3-manifolds along smooth boundaries and the role played by all flat connections in this operation.
NASA Astrophysics Data System (ADS)
Zheng, Xiang; Yang, Chao; Cai, Xiao-Chuan; Keyes, David
2015-03-01
We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn-Hilliard-Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton-Krylov-Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.
Zheng, Xiang; Yang, Chao; Cai, Xiao-Chuan; Keyes, David
2015-03-15
We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn–Hilliard–Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton–Krylov–Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.
Evaluation of the applicability of Helmholtz resonators for low frequency acoustic liners
NASA Astrophysics Data System (ADS)
Vanderwal, J. M. M.
1988-09-01
A literature study was performed on the acoustic behavior of those Helmholtz resonator type liners which are most promising for low frequency sound absorption in aero-engine applications. The equations for the acoustic impedance of various types of Helmholtz resonators were analyzed as well as the conditions for the validity of these equations. An experimental program is defined for a further analysis of various types of resonators.
Ge, Liang; Sotiropoulos, Fotis
2008-01-01
A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [1]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus. PMID:19194533
Ge, Liang; Sotiropoulos, Fotis
2007-08-01
A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [1]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus. PMID:19194533
NASA Astrophysics Data System (ADS)
Meulien Ohlmann, Odile
2013-02-01
Today the industry offers a chain of 3D products. Learning to "read" and to "create in 3D" becomes an issue of education of primary importance. 25 years professional experience in France, the United States and Germany, Odile Meulien set up a personal method of initiation to 3D creation that entails the spatial/temporal experience of the holographic visual. She will present some different tools and techniques used for this learning, their advantages and disadvantages, programs and issues of educational policies, constraints and expectations related to the development of new techniques for 3D imaging. Although the creation of display holograms is very much reduced compared to the creation of the 90ies, the holographic concept is spreading in all scientific, social, and artistic activities of our present time. She will also raise many questions: What means 3D? Is it communication? Is it perception? How the seeing and none seeing is interferes? What else has to be taken in consideration to communicate in 3D? How to handle the non visible relations of moving objects with subjects? Does this transform our model of exchange with others? What kind of interaction this has with our everyday life? Then come more practical questions: How to learn creating 3D visualization, to learn 3D grammar, 3D language, 3D thinking? What for? At what level? In which matter? for whom?
NASA Astrophysics Data System (ADS)
Bruno, Oscar P.; Cubillos, Max
2016-02-01
This paper introduces alternating-direction implicit (ADI) solvers of higher order of time-accuracy (orders two to six) for the compressible Navier-Stokes equations in two- and three-dimensional curvilinear domains. The higher-order accuracy in time results from 1) An application of the backward differentiation formulae time-stepping algorithm (BDF) in conjunction with 2) A BDF-like extrapolation technique for certain components of the nonlinear terms (which makes use of nonlinear solves unnecessary), as well as 3) A novel application of the Douglas-Gunn splitting (which greatly facilitates handling of boundary conditions while preserving higher-order accuracy in time). As suggested by our theoretical analysis of the algorithms for a variety of special cases, an extensive set of numerical experiments clearly indicate that all of the BDF-based ADI algorithms proposed in this paper are "quasi-unconditionally stable" in the following sense: each algorithm is stable for all couples (h , Δt)of spatial and temporal mesh sizes in a problem-dependent rectangular neighborhood of the form (0 ,Mh) × (0 ,Mt). In other words, for each fixed value of Δt below a certain threshold, the Navier-Stokes solvers presented in this paper are stable for arbitrarily small spatial mesh-sizes. The second-order formulation has further been rigorously shown to be unconditionally stable for linear hyperbolic and parabolic equations in two-dimensional space. Although implicit ADI solvers for the Navier-Stokes equations with nominal second-order of temporal accuracy have been proposed in the past, the algorithms presented in this paper are the first ADI-based Navier-Stokes solvers for which second-order or better accuracy has been verified in practice under non-trivial (non-periodic) boundary conditions.
Kaltenbacher, Barbara; Kaltenbacher, Manfred; Sim, Imbo
2013-01-01
We consider the second order wave equation in an unbounded domain and propose an advanced perfectly matched layer (PML) technique for its efficient and reliable simulation. In doing so, we concentrate on the time domain case and use the finite-element (FE) method for the space discretization. Our un-split-PML formulation requires four auxiliary variables within the PML region in three space dimensions. For a reduced version (rPML), we present a long time stability proof based on an energy analysis. The numerical case studies and an application example demonstrate the good performance and long time stability of our formulation for treating open domain problems. PMID:23888085
Kaltenbacher, Barbara; Kaltenbacher, Manfred; Sim, Imbo
2013-02-15
We consider the second order wave equation in an unbounded domain and propose an advanced perfectly matched layer (PML) technique for its efficient and reliable simulation. In doing so, we concentrate on the time domain case and use the finite-element (FE) method for the space discretization. Our un-split-PML formulation requires four auxiliary variables within the PML region in three space dimensions. For a reduced version (rPML), we present a long time stability proof based on an energy analysis. The numerical case studies and an application example demonstrate the good performance and long time stability of our formulation for treating open domain problems. PMID:23888085
NASA Astrophysics Data System (ADS)
Kaltenbacher, Barbara; Kaltenbacher, Manfred; Sim, Imbo
2013-02-01
We consider the second order wave equation in an unbounded domain and propose an advanced perfectly matched layer (PML) technique for its efficient and reliable simulation. In doing so, we concentrate on the time domain case and use the finite-element (FE) method for the space discretization. Our un-split-PML formulation requires four auxiliary variables within the PML region in three space dimensions. For a reduced version (rPML), we present a long time stability proof based on an energy analysis. The numerical case studies and an application example demonstrate the good performance and long time stability of our formulation for treating open domain problems.
NASA Astrophysics Data System (ADS)
Jia, Xuanji; Zhou, Yong
2015-09-01
We prove that a weak solution (u, b) to the MHD equations is smooth on (0, T ] if \\text{M}\\in {{L}α}≤ft(0,T;{{L}γ}≤ft({{{R}}3}\\right)\\right) with 2/α +3/γ =2 , 1≤slant α <∞ and 3/2<γ ≤slant ∞ , where \\text{M} is a 3× 3 mixture matrix (see its definition below). As we will explain later, this kind of regularity criteria is more likely to capture the nature of the coupling effects between the fluid velocity and the magnetic field in the evolution of the MHD flows. Moreover, the condition on \\text{M} is scaling invariant, i.e. it is of Ladyzhenskaya-Prodi-Serrin type.
ERIC Educational Resources Information Center
Hastings, S. K.
2002-01-01
Discusses 3 D imaging as it relates to digital representations in virtual library collections. Highlights include X-ray computed tomography (X-ray CT); the National Science Foundation (NSF) Digital Library Initiatives; output peripherals; image retrieval systems, including metadata; and applications of 3 D imaging for libraries and museums. (LRW)
NASA Astrophysics Data System (ADS)
Wang, Haogang; Liao, Tien-Hao; Shi, Jiancheng; Yu, Zherui
2014-11-01
The forthcoming Water Cycle Observation Mission (WCOM) is to understand the water cycle system among land, atmosphere, and ocean. In both active and passive microwave remote sensing of soil moisture, the surface roughness plays an important role. Electromagnetic models of roughness provide tables of emissivities and backscattering coefficients that can be used to retrieve soil moisture. In this paper, a fast and accurate three dimensional solution of Maxwell's equations is developed and employed to solve rough soil surface scattering problem at L-band. The algorithm combines QR Pre-Ranked Multilevel UV(MLUV) factorization and Hierarchical Fast Far Field Approximation. It is implemented using OpenMP interface for fast parallel calculation. In this algorithm, 1) QR based rank predetermined algorithm is derived to further compress the UV matrix pairs obtained using coarse-coarse sampling; 2) at the finer levels, MLUV is used straightforwardly to factorize the interactions between groups, while at the coarsest level, interactions between groups in the interaction list are calculated using an elegantly derived Hierarchical Fast Far Field Approximation (HFAFFA) to accelerate the calculation of interactions between large groups while keeping the accuracy of this approximation; 3) OpenMP interface is used to parallelize this new algorithm. Numerical results including the incoherent bistatic scattering coefficients and the emissivity demonstrate the efficiency of this method.
NASA Astrophysics Data System (ADS)
Fortes, A. Dominic; Suard, Emmanuelle; Lemée-Cailleau, Marie-Hélène; Pickard, Christopher J.; Needs, Richard J.
2009-10-01
We describe the results of a neutron powder diffraction study of perdeuterated ammonia monohydrate (AMH, ND3ṡD2O) carried out in the range 102
equation of state of AMH I has parameters, V0=248.00(2) Å3, K0=7.33(3) GPa with the first pressure derivative of K0 fixed at the value obtained in ab initio calculations, (∂K0/∂P)T=K0'=5.3; the implied value of the second derivative is therefore (∂2K0/∂P2)T=K0″=-0.94(1) GPa-1. At 351 MPa, we observed that the transition from AMH I to AMH II occurred over a period of 90 min, with an associated reduction in molar volume of 4.6% and an increase in the incompressibility of 19.6%.
Zaeytijd, J. de Bogaert, I.; Franchois, A.
2008-07-01
Electromagnetic scattering problems involving inhomogeneous objects can be numerically solved by applying a Method of Moments discretization to the volume integral equation. For electrically large problems, the iterative solution of the resulting linear system is expensive, both computationally and in memory use. In this paper, a hybrid MLFMA-FFT method is presented, which combines the fast Fourier transform (FFT) method and the High Frequency Multilevel Fast Multipole Algorithm (MLFMA) in order to reduce the cost of the matrix-vector multiplications needed in the iterative solver. The method represents the scatterers within a set of possibly disjoint identical cubic subdomains, which are meshed using a uniform cubic grid. This specific mesh allows for the application of FFTs to calculate the near interactions in the MLFMA and reduces the memory cost considerably, since the aggregation and disaggregation matrices of the MLFMA can be reused. Additional improvements to the general MLFMA framework, such as an extention of the FFT interpolation scheme of Sarvas et al. from the scalar to the vectorial case in combination with a more economical representation of the radiation patterns on the lowest level in vector spherical harmonics, are proposed and the choice of the subdomain size is discussed. The hybrid method performs better in terms of speed and memory use on large sparse configurations than both the FFT method and the HF MLFMA separately and it has lower memory requirements on general large problems. This is illustrated on a number of representative numerical test cases.
3D imaging of amplitude objects embedded in phase objects using transport of intensity
NASA Astrophysics Data System (ADS)
Banerjee, Partha; Basunia, Mahmudunnabi
2015-09-01
The amplitude and phase of the complex optical field in the Helmholtz equation obey a pair of coupled equations, arising from equating the real and imaginary parts. The imaginary part yields the transport of intensity equation (TIE), which can be used to derive the phase distribution at the observation plane. If a phase object is approximately imaged on the recording plane(s), TIE yields the phase without the need for phase unwrapping. In our experiment, the 3D image of a phase object and an amplitude object embedded in a phase object is recovered. The phase object is created by heating a liquid, comprising a solution of red dye in alcohol, using a focused 514 nm laser beam to the point where self-phase modulation of the beam is observed. The optical intensities are recorded at various planes during propagation of a low power 633 nm laser beam through the liquid. In the process of applying TIE to derive the phase at the observation plane, the real part of the complex equation is also examined as a cross-check of our calculations. For pure phase objects, it is shown that the real part of the complex equation is best satisfied around the image plane. Alternatively, it is proposed that this information can be used to determine the optimum image plane.
NASA Astrophysics Data System (ADS)
Ando, R.
2014-12-01
The boundary integral equation method formulated in the real space and time domain (BIEM-ST) has been used as a powerful tool to analyze the earthquake rupture dynamics on non-planar faults. Generally, BIEM is more accurate than volumetric methods such as the finite difference method and the finite difference method. With the recent development of the high performance computing environment, the earthquake rupture simulation studies have been conducted considering three dimensional realistic fault geometry models. However, the utility of BIEM-ST has been limited due to its heavy computational demanding increased depending on square of time steps (N2), which was needed to evaluate the historic integration. While BIEM can be efficient with the spectral domain formulation, the applications of such a method are limited to planar fault cases. In this study, we propose a new method to reduce the calculation time of BIEM-ST to linear of time step (N) without degrading the accuracy in the 3 dimensional modeling space. We extends the method proposed earlier for the case of the 2 dimensional framework, applying the asymptotic expressions of the elasto-dynamic Green's functions. This method uses the physical nature of the stress Green's function as dividing the causality cone according to the distances from the wave-fronts. The scalability of this method is shown on the parallel computing environment of the distributed memory. We demonstrate the applicability to analyses of subduction earthquake cases, suffering long time from the numerical limitations of previously available BIEMs. We analyze the dynamic rupture processes on dipping reverse faults embed in a three dimensional elastic half space.
Crandall, K.R.
1987-08-01
TRACE 3-D is an interactive beam-dynamics program that calculates the envelopes of a bunched beam, including linear space-charge forces, through a user-defined transport system. TRACE 3-D provides an immediate graphics display of the envelopes and the phase-space ellipses and allows nine types of beam-matching options. This report describes the beam-dynamics calculations and gives detailed instruction for using the code. Several examples are described in detail.
Helmholtz solitons at nonlinear interfaces.
Sánchez-Curto, J; Chamorro-Posada, P; McDonald, G S
2007-05-01
Reflection and refraction of spatial solitons at dielectric interfaces, accommodating arbitrarily angles of incidence, is studied. Analysis is based on Helmholtz soliton theory, which eliminates the angular restriction associated with the paraxial approximation. A novel generalization of Snell's law is discovered that is valid for collimated light beams and the entire angular domain. Our new theoretical predictions are shown to be in excellent agreement with full numerical simulations. New qualitative features of soliton refraction and limitations of previous paraxial analyses are highlighted. PMID:17410257
NASA Astrophysics Data System (ADS)
Brüning, J.; Dobrokhotov, S. Yu.; Minenkov, D. S.
2011-12-01
The aim of this paper is to construct solutions of the Dirichlet problem for the 3D Laplace equation in a layer with highly oscillating boundary. The boundary simulates the surface of a nanotube array, and the solutions are applied to compute the cold field electron emission. We suggest a family of exact solutions that solve the problem for a boundary with appropriate geometry. These solutions, along with the Fowler-Nordheim formula, allow one to present explicit asymptotic formulas for the electric field and the emission current. In this part of the paper, we consider the main mathematical aspects, restricting ourselves to the analysis of properties of the potential created by a single tube and a regular array of tubes. In the next part, we shall consider some cases corresponding to nonregular arrays of tubes and concrete physical examples.
Acoustic control in enclosures using optimally designed Helmholtz resonators
NASA Astrophysics Data System (ADS)
Driesch, Patricia Lynne
A virtual design methodology is developed to minimize the noise in enclosures with optimally designed, passive, acoustic absorbers (Helmholtz resonators). A series expansion of eigen functions is used to represent the acoustic absorbers as external volume velocities, eliminating the need for a solution of large matrix eigen value problems. A determination of this type (efficient model/reevaluation approach) significantly increases the design possibilities when optimization techniques are implemented. As a benchmarking exercise, this novel methodology was experimentally validated for a narrowband acoustic assessment of two optimally designed Helmholtz resonators coupled to a 2D enclosure. The resonators were tuned to the two lowest resonance frequencies of a 30.5 by 40.6 by 2.5 cm (12 x 16 x 1 inch) cavity with the resonator volume occupying only 2% of the enclosure volume. A maximum potential energy reduction of 12.4 dB was obtained at the second resonance of the cavity. As a full-scale demonstration of the efficacy of the proposed design method, the acoustic response from 90--190 Hz of a John Deere 7000 Ten series tractor cabin was investigated. The lowest cabin mode, referred to as a "boom" mode, proposes a significant challenge to a noise control engineer since its anti-node is located near the head of the operator and often generates unacceptable sound pressure levels. Exploiting the low frequency capability of Helmholtz resonators, lumped parameter models of these resonators were coupled to the enclosure via an experimentally determined acoustic model of the tractor cabin. The virtual design methodology uses gradient optimization techniques as a post processor for the modeling and analysis of the unmodified acoustic interior to determine optimal resonator characteristics. Using two optimally designed Helmholtz resonators; potential energy was experimentally reduced by 3.4 and 10.3 dB at 117 and 167 Hz, respectively.
NASA Astrophysics Data System (ADS)
Oldham, Mark
2015-01-01
Radiochromic materials exhibit a colour change when exposed to ionising radiation. Radiochromic film has been used for clinical dosimetry for many years and increasingly so recently, as films of higher sensitivities have become available. The two principle advantages of radiochromic dosimetry include greater tissue equivalence (radiologically) and the lack of requirement for development of the colour change. In a radiochromic material, the colour change arises direct from ionising interactions affecting dye molecules, without requiring any latent chemical, optical or thermal development, with important implications for increased accuracy and convenience. It is only relatively recently however, that 3D radiochromic dosimetry has become possible. In this article we review recent developments and the current state-of-the-art of 3D radiochromic dosimetry, and the potential for a more comprehensive solution for the verification of complex radiation therapy treatments, and 3D dose measurement in general.
NASA Astrophysics Data System (ADS)
Iliesiu, Luca; Kos, Filip; Poland, David; Pufu, Silviu S.; Simmons-Duffin, David; Yacoby, Ran
2016-03-01
We study the conformal bootstrap for a 4-point function of fermions < ψψψψ> in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ × ψ OPE, and also on the central charge C T . We observe features in our bounds that coincide with scaling dimensions in the GrossNeveu models at large N . We also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.
Clement, T.P.; Jones, N.L.
1998-02-01
RT3D (Reactive Transport in 3-Dimensions) is a computer code that solves coupled partial differential equations that describe reactive-flow and transport of multiple mobile and/or immobile species in a three dimensional saturated porous media. RT3D was developed from the single-species transport code, MT3D (DoD-1.5, 1997 version). As with MT3D, RT3D also uses the USGS groundwater flow model MODFLOW for computing spatial and temporal variations in groundwater head distribution. This report presents a set of tutorial problems that are designed to illustrate how RT3D simulations can be performed within the Department of Defense Groundwater Modeling System (GMS). GMS serves as a pre- and post-processing interface for RT3D. GMS can be used to define all the input files needed by RT3D code, and later the code can be launched from within GMS and run as a separate application. Once the RT3D simulation is completed, the solution can be imported to GMS for graphical post-processing. RT3D v1.0 supports several reaction packages that can be used for simulating different types of reactive contaminants. Each of the tutorials, described below, provides training on a different RT3D reaction package. Each reaction package has different input requirements, and the tutorials are designed to describe these differences. Furthermore, the tutorials illustrate the various options available in GMS for graphical post-processing of RT3D results. Users are strongly encouraged to complete the tutorials before attempting to use RT3D and GMS on a routine basis.
Monolithically integrated Helmholtz coils by 3-dimensional printing
Li, Longguang; Abedini-Nassab, Roozbeh; Yellen, Benjamin B.
2014-06-23
3D printing technology is of great interest for the monolithic fabrication of integrated systems; however, it is a challenge to introduce metallic components into 3D printed molds to enable broader device functionality. Here, we develop a technique for constructing a multi-axial Helmholtz coil by injecting a eutectic liquid metal Gallium Indium alloy (EGaIn) into helically shaped orthogonal cavities constructed in a 3D printed block. The tri-axial solenoids each carry up to 3.6 A of electrical current and produce magnetic field up to 70 G. Within the central section of the coil, the field variation is less than 1% and is in agreement with theory. The flow rates and critical pressures required to fill the 3D cavities with liquid metal also agree with theoretical predictions and provide scaling trends for filling the 3D printed parts. These monolithically integrated solenoids may find future applications in electronic cell culture platforms, atomic traps, and miniaturized chemical analysis systems based on nuclear magnetic resonance.
Software for 3D radiotherapy dosimetry. Validation
NASA Astrophysics Data System (ADS)
Kozicki, Marek; Maras, Piotr; Karwowski, Andrzej C.
2014-08-01
The subject of this work is polyGeVero® software (GeVero Co., Poland), which has been developed to fill the requirements of fast calculations of 3D dosimetry data with the emphasis on polymer gel dosimetry for radiotherapy. This software comprises four workspaces that have been prepared for: (i) calculating calibration curves and calibration equations, (ii) storing the calibration characteristics of the 3D dosimeters, (iii) calculating 3D dose distributions in irradiated 3D dosimeters, and (iv) comparing 3D dose distributions obtained from measurements with the aid of 3D dosimeters and calculated with the aid of treatment planning systems (TPSs). The main features and functions of the software are described in this work. Moreover, the core algorithms were validated and the results are presented. The validation was performed using the data of the new PABIGnx polymer gel dosimeter. The polyGeVero® software simplifies and greatly accelerates the calculations of raw 3D dosimetry data. It is an effective tool for fast verification of TPS-generated plans for tumor irradiation when combined with a 3D dosimeter. Consequently, the software may facilitate calculations by the 3D dosimetry community. In this work, the calibration characteristics of the PABIGnx obtained through four calibration methods: multi vial, cross beam, depth dose, and brachytherapy, are discussed as well.
Hong, X; Gao, H
2014-06-15
Purpose: The Linear Boltzmann Transport Equation (LBTE) solved through statistical Monte Carlo (MC) method provides the accurate dose calculation in radiotherapy. This work is to investigate the alternative way for accurately solving LBTE using deterministic numerical method due to its possible advantage in computational speed from MC. Methods: Instead of using traditional spherical harmonics to approximate angular scattering kernel, our deterministic numerical method directly computes angular scattering weights, based on a new angular discretization method that utilizes linear finite element method on the local triangulation of unit angular sphere. As a Result, our angular discretization method has the unique advantage in positivity, i.e., to maintain all scattering weights nonnegative all the time, which is physically correct. Moreover, our method is local in angular space, and therefore handles the anisotropic scattering well, such as the forward-peaking scattering. To be compatible with image-guided radiotherapy, the spatial variables are discretized on the structured grid with the standard diamond scheme. After discretization, the improved sourceiteration method is utilized for solving the linear system without saving the linear system to memory. The accuracy of our 3D solver is validated using analytic solutions and benchmarked with Geant4, a popular MC solver. Results: The differences between Geant4 solutions and our solutions were less than 1.5% for various testing cases that mimic the practical cases. More details are available in the supporting document. Conclusion: We have developed a 3D LBTE solver based on a new angular discretization method that guarantees the positivity of scattering weights for physical correctness, and it has been benchmarked with Geant4 for photon dose calculation.
NASA Astrophysics Data System (ADS)
Iizuka, Keigo
2008-02-01
In order to circumvent the fact that only one observer can view the image from a stereoscopic microscope, an attachment was devised for displaying the 3D microscopic image on a large LCD monitor for viewing by multiple observers in real time. The principle of operation, design, fabrication, and performance are presented, along with tolerance measurements relating to the properties of the cellophane half-wave plate used in the design.
Fluid mechanical model of the Helmholtz resonator
NASA Technical Reports Server (NTRS)
Hersh, A. S.; Walker, B.
1977-01-01
A semi-empirical fluid mechanical model of the acoustic behavior of Helmholtz resonators is presented which predicts impedance as a function of the amplitude and frequency of the incident sound pressure field and resonator geometry. The model assumes that the particle velocity approaches the orifice in a spherical manner. The incident and cavity sound fields are connected by solving the governing oscillating mass and momentum conservation equations. The model is in agreement with the Rayleigh slug-mass model at low values of incident sound pressure level. At high values, resistance is predicted to be independent of frequency, proportional to the square root of the amplitude of the incident sound pressure field, and virtually independent of resonator geometry. Reactance is predicted to depend in a very complicated way upon resonator geometry, incident sound pressure level, and frequency. Nondimensional parameters are defined that divide resonator impedance into three categories corresponding to low, moderately low, and intense incident sound pressure amplitudes. The two-microphone method was used to measure the impedance of a variety of resonators. The data were used to refine and verify the model.
A tunable electromechanical Helmholtz resonator
NASA Astrophysics Data System (ADS)
Liu, Fei
Acoustic liners are used in turbofan engine nacelles for the suppression of engine noise. For a given engine, there are different optimum impedance distributions associated with take-off, cut-back, and approach flight conditions. The impedance of conventional acoustic liners is fixed for a given geometry, and conventional active liner approaches are impractical. This project addresses the need for a tunable impedance through the development of an electromechanical Helmholtz resonator (EMHR). The device consists of a Helmholtz resonator with the standard rigid backplate replaced by a compliant piezoelectric composite. Analytical models (i.e., a lumped element model (LEM) and a transfer matrix (TM) representation of the EMHR) are developed to predict the acoustic behavior of the EMHR. The EMHR is experimentally investigated using the standard two-microphone method (TMM). The measurement results validate both the LEM and the TM of the EMHR. Good agreement between predicted and measured impedance is obtained. Short- and open-circuit loads define the limits of the tuning range using resistive and capacitive loads. There is approximately a 9% tuning limit under these conditions for the non-optimized resonator configuration studied. Inductive shunt loads result in a 3 degree-of-freedom (DOF) system and an enhanced tuning range of over 47% that is not restricted by the short- and open-circuit limits. Damping coefficient measurements for a piezoelectric backplate in a vacuum chamber are performed and indicate that the damping is dominated by structural damping losses. A Pareto optimization design based on models of the EMHR is performed with non-inductive loads. The EMHR with non-inductive loads has 2DOF and two resonant frequencies. The tuning ranges of the two resonant frequencies of the EMHR with non-inductive loads cannot be optimized simultaneously, so a trade-off (Pareto solution) must be reached. The Pareto solution shows how design trade-offs can be used to satisfy
NASA Astrophysics Data System (ADS)
Kostrzewski, Andrew A.; Aye, Tin M.; Kim, Dai Hyun; Esterkin, Vladimir; Savant, Gajendra D.
1998-09-01
Physical Optics Corporation has developed an advanced 3-D virtual reality system for use with simulation tools for training technical and military personnel. This system avoids such drawbacks of other virtual reality (VR) systems as eye fatigue, headaches, and alignment for each viewer, all of which are due to the need to wear special VR goggles. The new system is based on direct viewing of an interactive environment. This innovative holographic multiplexed screen technology makes it unnecessary for the viewer to wear special goggles.
NASA Technical Reports Server (NTRS)
1992-01-01
Ames Research Center research into virtual reality led to the development of the Convolvotron, a high speed digital audio processing system that delivers three-dimensional sound over headphones. It consists of a two-card set designed for use with a personal computer. The Convolvotron's primary application is presentation of 3D audio signals over headphones. Four independent sound sources are filtered with large time-varying filters that compensate for motion. The perceived location of the sound remains constant. Possible applications are in air traffic control towers or airplane cockpits, hearing and perception research and virtual reality development.
De Kock, Liesbet
2016-04-01
In this analysis, the classical problem of Hermann von Helmholtz's (1821-1894) Kantianism is explored from a particular vantage point, that to my knowledge, has not received the attention it deserves notwithstanding its possible key role in disentangling Helmholtz's relation to Kant's critical project. More particularly, we will focus on Helmholtz's critical engagement with Kant's concept of intuition [Anschauung] and (the related issue of) his dissatisfaction with Kant's doctrinal dualism. In doing so, it soon becomes clear that both (i) crucially mediated Helmholtz's idiosyncratic appropriation and criticism of (certain aspects of) Kant's critical project, and (ii) can be considered as a common denominator in a variety of issues that are usually addressed separately under the general header of (the problem of) Helmholtz's Kantianism. The perspective offered in this analysis can not only shed interesting new light on some interpretive issues that have become commonplace in discussions on Helmholtz's Kantianism, but also offers a particular way of connecting seemingly unrelated dimensions of Helmholtz's engagement with Kant's critical project (e.g. Helmholtz's views on causality and space). Furthermore, it amounts to the rather surprising conclusion that Helmholtz's most drastic revision of Kant's project pertains to his assumption of free will as a formal condition of experience and knowledge. PMID:27083081
Cevidanes, Lucia; Tucker, Scott; Styner, Martin; Kim, Hyungmin; Chapuis, Jonas; Reyes, Mauricio; Proffit, William; Turvey, Timothy; Jaskolka, Michael
2009-01-01
This paper discusses the development of methods for computer-aided jaw surgery. Computer-aided jaw surgery allows us to incorporate the high level of precision necessary for transferring virtual plans into the operating room. We also present a complete computer-aided surgery (CAS) system developed in close collaboration with surgeons. Surgery planning and simulation include construction of 3D surface models from Cone-beam CT (CBCT), dynamic cephalometry, semi-automatic mirroring, interactive cutting of bone and bony segment repositioning. A virtual setup can be used to manufacture positioning splints for intra-operative guidance. The system provides further intra-operative assistance with the help of a computer display showing jaw positions and 3D positioning guides updated in real-time during the surgical procedure. The CAS system aids in dealing with complex cases with benefits for the patient, with surgical practice, and for orthodontic finishing. Advanced software tools for diagnosis and treatment planning allow preparation of detailed operative plans, osteotomy repositioning, bone reconstructions, surgical resident training and assessing the difficulties of the surgical procedures prior to the surgery. CAS has the potential to make the elaboration of the surgical plan a more flexible process, increase the level of detail and accuracy of the plan, yield higher operative precision and control, and enhance documentation of cases. Supported by NIDCR DE017727, and DE018962 PMID:20816308
3D Global Two-Fluid Simulations of Turbulence in LAPD
NASA Astrophysics Data System (ADS)
Fisher, Dustin; Rogers, Barrett; Ricci, Paolo
2012-10-01
3D global two-fluid simulations are presented in an ongoing effort to identify and understand the physics of instabilities that arise in the Large Plasma Device (LAPD) at UCLA's Basic Science Facility. The LAPD, with its wide range of tunable parameters and device configurations, is ideally suited for studying space and laboratory plasmas. Moreover, the highly detailed and reproducible measurements of the LAPD lend themselves amicably to comparisons with simulations. Ongoing modeling is done using a modified version of the Global Braginskii Solver (GBS) [1] that models the plasma from source to edge region in a fully 3D two-fluid code. The reduced Braginskii equations are solved on a field-aligned grid using a finite difference method and 4th order Runge-Kutta time stepping and are parallelized on Dartmouth's Discovery cluster. Recent progress has been made to account for the thermionic cathode emission of fast electrons at the source, the axial dependence of the plasma source, and it is now possible to vary the potential on the front and side walls. Preliminary results, seen from the density and temperature profiles, show that the low frequency Kelvin Helmholtz instability still dominates the turbulence in the device.[4pt] [1] B. Rogers and P. Ricci. Phys. Rev. Lett. 104:225002, 2010
A transverse Kelvin-Helmholtz instability in a magnetized plasma
NASA Technical Reports Server (NTRS)
Kintner, P.; Dangelo, N.
1977-01-01
An analysis is conducted of the transverse Kelvin-Helmholtz instability in a magnetized plasma for unstable flute modes. The analysis makes use of a two-fluid model. Details regarding the instability calculation are discussed, taking into account the ion continuity and momentum equations, the solution of a zero-order and a first-order component, and the properties of the solution. It is expected that the linear calculation conducted will apply to situations in which the plasma has experienced no more than a few growth periods.
Parametric design of tri-axial nested Helmholtz coils
Abbott, Jake J.
2015-05-15
This paper provides an optimal parametric design for tri-axial nested Helmholtz coils, which are used to generate a uniform magnetic field with controllable magnitude and direction. Circular and square coils, both with square cross section, are considered. Practical considerations such as wire selection, wire-wrapping efficiency, wire bending radius, choice of power supply, and inductance and time response are included. Using the equations provided, a designer can quickly create an optimal set of custom coils to generate a specified field magnitude in the uniform-field region while maintaining specified accessibility to the central workspace. An example case study is included.
NASA Astrophysics Data System (ADS)
Gil, José J.; San José, Ignacio
2010-11-01
From our previous definition of the indices of polarimetric purity for 3D light beams [J.J. Gil, J.M. Correas, P.A. Melero and C. Ferreira, Monogr. Semin. Mat. G. de Galdeano 31, 161 (2004)], an analysis of their geometric and physical interpretation is presented. It is found that, in agreement with previous results, the first parameter is a measure of the degree of polarization, whereas the second parameter (called the degree of directionality) is a measure of the mean angular aperture of the direction of propagation of the corresponding light beam. This pair of invariant, non-dimensional, indices of polarimetric purity contains complete information about the polarimetric purity of a light beam. The overall degree of polarimetric purity is obtained as a weighted quadratic average of the degree of polarization and the degree of directionality.
Caspi, S.; Helm, M.; Laslett, L.J.
1991-03-30
We have developed an harmonic representation for the three dimensional field components within the windings of accelerator magnets. The form by which the field is presented is suitable for interfacing with other codes that make use of the 3D field components (particle tracking and stability). The field components can be calculated with high precision and reduced cup time at any location (r,{theta},z) inside the magnet bore. The same conductor geometry which is used to simulate line currents is also used in CAD with modifications more readily available. It is our hope that the format used here for magnetic fields can be used not only as a means of delivering fields but also as a way by which beam dynamics can suggest correction to the conductor geometry. 5 refs., 70 figs.
NASA Technical Reports Server (NTRS)
2004-01-01
The Mars Exploration Rover Spirit took this 3-D navigation camera mosaic of the crater called 'Bonneville' after driving approximately 13 meters (42.7 feet) to get a better vantage point. Spirit's current position is close enough to the edge to see the interior of the crater, but high enough and far enough back to get a view of all of the walls. Because scientists and rover controllers are so pleased with this location, they will stay here for at least two more martian days, or sols, to take high resolution panoramic camera images of 'Bonneville' in its entirety. Just above the far crater rim, on the left side, is the rover's heatshield, which is visible as a tiny reflective speck.
High-Accuracy Finite Difference Equations for Simulation of Photonic Structures
Hadley, G.R.
1999-04-23
Progress towards the development of such algorithms as been reported for waveguide analysis'-3and vertical-cavity laser simulation. In all these cases, the higher accuracy order was obtained for a single spatial dimension. More recently, this concept was extended to differencing of the Helmholtz Equation on a 2-D grid, with uniform regions treated to 4th order and dielectric interfaces to 3'd order5. No attempt was made to treat corners properly. In this talk I will describe the extension of this concept to allow differencing of the Helmholtz Equation on a 2-D grid to 6* order in uniform regions and 5* order at dielectric interfaces. In addition, the first known derivation of a finite difference equation for a dielectric comer that allows correct satisfaction of all boundary conditions will be presented. This equation is only accurate to first order, but as will be shown, results in simulations that are third-order-accurate. In contrast to a previous approach3 that utilized a generalized Douglas scheme to increase the accuracy order of the difference second derivative, the present method invokes the Helmholtz Equation itself to convert derivatives of high order in a single direction into mixed
Kelvin-Helmholtz instabilities with Godunov smoothed particle hydrodynamics
NASA Astrophysics Data System (ADS)
Cha, Seung-Hoon; Inutsuka, Shu-Ichiro; Nayakshin, Sergei
2010-04-01
Numerical simulations for the non-linear development of Kelvin-Helmholtz instability in two different density layers have been performed with the particle-based method (Godunov SPH) developed by Inutsuka. The Godunov SPH can describe the Kelvin-Helmholtz instability even with a high-density contrast, while the standard SPH shows the absence of the instability across a density gradient. The interaction of a dense blob with a hot ambient medium has been performed also. The Godunov SPH describes the formation and evolution of the fingers due to the combinations of Rayleigh-Taylor, Richtmyer-Meshkov and Kelvin-Helmholtz instabilities. The blob test result coincides well with the results of the grid-based codes. An inaccurate handling of a density gradient in the standard SPH has been pointed out as the direct reason of the absence of the instabilities. An unphysical force happens at the density gradient even in a pressure equilibrium, and repulses particles from the initial density discontinuity. Therefore, the initial perturbation damps, and a gap form at the discontinuity. The unphysical force has been studied in terms of the consistency of a numerical scheme. Contrary to the standard SPH, the momentum equation of the Godunov SPH does not use the particle approximation, and has been derived from the kernel convolution or a new Lagrangian function. The new Lagrangian function used in the Godunov SPH is more analogous to the real Lagrangian function for continuum. The momentum equation of the Godunov SPH has much better linear consistency, so the unphysical force is greatly reduced compared to the standard SPH in a high density contrast.
NASA Technical Reports Server (NTRS)
1997-01-01
Many prominent rocks near the Sagan Memorial Station are featured in this image, taken in stereo by the Imager for Mars Pathfinder (IMP) on Sol 3. 3D glasses are necessary to identify surface detail. Wedge is at lower left; Shark, Half-Dome, and Pumpkin are at center. Flat Top, about four inches high, is at lower right. The horizon in the distance is one to two kilometers away.
Mars Pathfinder is the second in NASA's Discovery program of low-cost spacecraft with highly focused science goals. The Jet Propulsion Laboratory, Pasadena, CA, developed and manages the Mars Pathfinder mission for NASA's Office of Space Science, Washington, D.C. JPL is an operating division of the California Institute of Technology (Caltech). The Imager for Mars Pathfinder (IMP) was developed by the University of Arizona Lunar and Planetary Laboratory under contract to JPL. Peter Smith is the Principal Investigator.
Click below to see the left and right views individually. [figure removed for brevity, see original site] Left [figure removed for brevity, see original site] Right
NASA Technical Reports Server (NTRS)
2004-01-01
This 3-D, microscopic imager mosaic of a target area on a rock called 'Diamond Jenness' was taken after NASA's Mars Exploration Rover Opportunity ground into the surface with its rock abrasion tool for a second time.
Opportunity has bored nearly a dozen holes into the inner walls of 'Endurance Crater.' On sols 177 and 178 (July 23 and July 24, 2004), the rover worked double-duty on Diamond Jenness. Surface debris and the bumpy shape of the rock resulted in a shallow and irregular hole, only about 2 millimeters (0.08 inch) deep. The final depth was not enough to remove all the bumps and leave a neat hole with a smooth floor. This extremely shallow depression was then examined by the rover's alpha particle X-ray spectrometer.
On Sol 178, Opportunity's 'robotic rodent' dined on Diamond Jenness once again, grinding almost an additional 5 millimeters (about 0.2 inch). The rover then applied its Moessbauer spectrometer to the deepened hole. This double dose of Diamond Jenness enabled the science team to examine the rock at varying layers. Results from those grindings are currently being analyzed.
The image mosaic is about 6 centimeters (2.4 inches) across.
Extraordinary acoustic transmission mediated by Helmholtz resonators
Koju, Vijay; Rowe, Ebony; Robertson, William M.
2014-07-15
We demonstrate perfect transmission of sound through a rigid barrier embedded with Helmholtz resonators. The resonators are confined within a waveguide and they are oriented such that one neck protrudes onto each side of the barrier. Perfect sound transmission occurs even though the open area of the necks is less than 3% of the barrier area. Maximum transmission occurs at the resonant frequency of the Helmholtz resonator. Because the dimensions of the Helmholtz resonators are much smaller than the resonant wavelength, the transmission is independent of the direction of sound on the barrier and of the relative placement of the necks. Further, we show that the transmitted sound experiences a continuous phase transition of π radians as a function of frequency through resonance. In simulations of adjacent resonators with slightly offset resonance frequencies, the phase difference leads to destructive interference. By expanding the simulation to a linear array of tuned Helmholtz resonators we show that it is possible to create an acoustic lens. The ability of Helmholtz resonator arrays to manipulate the phase of a plane acoustic wave enables a new class of sonic beam-forming devices analogous to diffractive optics.
Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.
Kiselev, Aleksei P; Plachenov, Alexandr B
2016-04-01
The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given. PMID:27140777
Theory of a generalized Helmholtz resonator.
NASA Technical Reports Server (NTRS)
Tang, P. K.; Sirignano, W. A.
1973-01-01
Based on the jet-flow model which is manifested in the nonlinearity of the orifice flow upon the passage of a high intensity wave, the theory of a generalized Helmholtz resonator has been developed. The results for some special devices, such as the conventional Helmholtz resonator and the quarter-wave tube, can be obtained through this general approach. The performance of the acoustic damper is characterized by a quantity known as the real part of the admittance coefficient. It is known that the conventional Helmholtz resonator has the lowest peak performance but the response is quite flat over a certain frequency range. On the other hand, a quarter-wave tube offers the largest peak in energy absorption with rather poor off-resonance behavior. Once the orifice length goes beyond the quarter-wave tube configuration, the performance of the so-called long damping device is even less attractive away from resonance.
Helmholtz and the psychophysiology of time.
Debru, C
2001-09-01
After having measured the velocity of the nervous impulse in the 1850s, Helmholtz began doing research on the temporal dimensions of visual perception. Experiments dealing with the velocity of propagation in nerves (as well as with aspects of perception) were carried out occasionally for some fifteen years until their final publication in 1871. Although the temporal dimension of perception seems to have interested Helmholtz less than problems of geometry and space, his experiments on the time of perception were technically rather subtle and seminal, especially compared with experiments performed by his contemporaries, such as Sigmund Exner, William James, Rudolf Hermann Lotze, Ernst Mach, Wilhelm Volkmann, and Wilhelm Wundt. Helmholtz's conception of the temporal aspects of perception reflects the continuity that holds between psychophysiological research and the Kantian philosophical background. PMID:12068897
Large Eddy Simulations of Kelvin-Helmholtz Instabilities in Stratified Ocean Flows
NASA Astrophysics Data System (ADS)
Brown, Dana; Goodman, Louis; Raessi, Mehdi
2012-11-01
Numerical simulations of turbulence in the ocean environment are used to supplement and enhance understanding of observational data. Here, using the NGA framework (Dejardins et al., JCP 2008), direct numerical simulations (DNS) and large eddy simulations (LES) of Kelvin-Helmholtz instabilities are employed to study turbulence in presence of density stratification. Kelvin-Helmholtz instabilities have been shown to be a common source of turbulence in the ocean. Past DNS studies of Kelvin Helmholtz instabilities have compared favorably with observational data, but were limited to moderate Reynolds numbers. Here, LES is used to solve the filtered incompressible NS equations at a higher Reynolds number, Re = 10,000. The effect of increased Reynolds number on the turbulence behavior is examined in terms of velocity spectra and energy budgets.
3D Elastic Wavefield Tomography
NASA Astrophysics Data System (ADS)
Guasch, L.; Warner, M.; Stekl, I.; Umpleby, A.; Shah, N.
2010-12-01
Wavefield tomography, or waveform inversion, aims to extract the maximum information from seismic data by matching trace by trace the response of the solid earth to seismic waves using numerical modelling tools. Its first formulation dates from the early 80's, when Albert Tarantola developed a solid theoretical basis that is still used today with little change. Due to computational limitations, the application of the method to 3D problems has been unaffordable until a few years ago, and then only under the acoustic approximation. Although acoustic wavefield tomography is widely used, a complete solution of the seismic inversion problem requires that we account properly for the physics of wave propagation, and so must include elastic effects. We have developed a 3D tomographic wavefield inversion code that incorporates the full elastic wave equation. The bottle neck of the different implementations is the forward modelling algorithm that generates the synthetic data to be compared with the field seismograms as well as the backpropagation of the residuals needed to form the direction update of the model parameters. Furthermore, one or two extra modelling runs are needed in order to calculate the step-length. Our approach uses a FD scheme explicit time-stepping by finite differences that are 4th order in space and 2nd order in time, which is a 3D version of the one developed by Jean Virieux in 1986. We chose the time domain because an explicit time scheme is much less demanding in terms of memory than its frequency domain analogue, although the discussion of wich domain is more efficient still remains open. We calculate the parameter gradients for Vp and Vs by correlating the normal and shear stress wavefields respectively. A straightforward application would lead to the storage of the wavefield at all grid points at each time-step. We tackled this problem using two different approaches. The first one makes better use of resources for small models of dimension equal
NASA Astrophysics Data System (ADS)
Wu, Chensheng; Nelson, William; Davis, Christopher C.
2014-10-01
Plenoptic functions are functions that preserve all the necessary light field information of optical events. Theoretical work has demonstrated that geometric based plenoptic functions can serve equally well in the traditional wave propagation equation known as the "scalar stochastic Helmholtz equation". However, in addressing problems of 3D turbulence simulation, the dominant methods using phase screen models have limitations both in explaining the choice of parameters (on the transverse plane) in real-world measurements, and finding proper correlations between neighboring phase screens (the Markov assumption breaks down). Though possible corrections to phase screen models are still promising, the equivalent geometric approach based on plenoptic functions begins to show some advantages. In fact, in these geometric approaches, a continuous wave problem is reduced to discrete trajectories of rays. This allows for convenience in parallel computing and guarantees conservation of energy. Besides the pairwise independence of simulated rays, the assigned refractive index grids can be directly tested by temperature measurements with tiny thermoprobes combined with other parameters such as humidity level and wind speed. Furthermore, without loss of generality one can break the causal chain in phase screen models by defining regional refractive centers to allow rays that are less affected to propagate through directly. As a result, our work shows that the 3D geometric approach serves as an efficient and accurate method in assessing relevant turbulence problems with inputs of several environmental measurements and reasonable guesses (such as Cn 2 levels). This approach will facilitate analysis and possible corrections in lateral wave propagation problems, such as image de-blurring, prediction of laser propagation over long ranges, and improvement of free space optic communication systems. In this paper, the plenoptic function model and relevant parallel algorithm computing
NASA Astrophysics Data System (ADS)
Mediavilla, Evencio; Arribas, Santiago; Roth, Martin; Cepa-Nogué, Jordi; Sánchez, Francisco
2011-09-01
Preface; Acknowledgements; 1. Introductory review and technical approaches Martin M. Roth; 2. Observational procedures and data reduction James E. H. Turner; 3. 3D Spectroscopy instrumentation M. A. Bershady; 4. Analysis of 3D data Pierre Ferruit; 5. Science motivation for IFS and galactic studies F. Eisenhauer; 6. Extragalactic studies and future IFS science Luis Colina; 7. Tutorials: how to handle 3D spectroscopy data Sebastian F. Sánchez, Begona García-Lorenzo and Arlette Pécontal-Rousset.
3D Elevation Program—Virtual USA in 3D
Lukas, Vicki; Stoker, J.M.
2016-01-01
The U.S. Geological Survey (USGS) 3D Elevation Program (3DEP) uses a laser system called ‘lidar’ (light detection and ranging) to create a virtual reality map of the Nation that is very accurate. 3D maps have many uses with new uses being discovered all the time.
De Kock, Liesbet
2014-12-01
This paper aims at contributing to the ongoing efforts to get a firmer grasp of the systematic significance of the entanglement of idealism and empiricism in Helmholtz's work. Contrary to existing analyses, however, the focal point of the present exposition is Helmholtz's attempt to articulate a psychological account of objectification. Helmholtz's motive, as well as his solution to the problem of the object are outlined, and interpreted against the background of his scientific practice on the one hand, and that of empiricist and (transcendental) idealist analyses of experience on the other. The specifically psychological angle taken, not only prompts us to consider figures who have hitherto been treated as having only minor import for Helmholtz interpretation (most importantly J.S. Mill and J.G. Fichte), it furthermore sheds new light on some central tenets of the latter's psychological stance that have hitherto remained underappreciated. For one thing, this analysis reveals an explicit voluntarist tendency in Helmholtz's psychological theory. In conclusion, it is argued that the systematic significance of Helmholtz's empirico-transcendentalism with respect to questions of the mind is best understood as an attempt to found his empirical theory of perception in a second order, normative account of epistemic subjectivity. PMID:25549449
Concurrent 3-D motion segmentation and 3-D interpretation of temporal sequences of monocular images.
Sekkati, Hicham; Mitiche, Amar
2006-03-01
The purpose of this study is to investigate a variational method for joint multiregion three-dimensional (3-D) motion segmentation and 3-D interpretation of temporal sequences of monocular images. Interpretation consists of dense recovery of 3-D structure and motion from the image sequence spatiotemporal variations due to short-range image motion. The method is direct insomuch as it does not require prior computation of image motion. It allows movement of both viewing system and multiple independently moving objects. The problem is formulated following a variational statement with a functional containing three terms. One term measures the conformity of the interpretation within each region of 3-D motion segmentation to the image sequence spatiotemporal variations. The second term is of regularization of depth. The assumption that environmental objects are rigid accounts automatically for the regularity of 3-D motion within each region of segmentation. The third and last term is for the regularity of segmentation boundaries. Minimization of the functional follows the corresponding Euler-Lagrange equations. This results in iterated concurrent computation of 3-D motion segmentation by curve evolution, depth by gradient descent, and 3-D motion by least squares within each region of segmentation. Curve evolution is implemented via level sets for topology independence and numerical stability. This algorithm and its implementation are verified on synthetic and real image sequences. Viewers presented with anaglyphs of stereoscopic images constructed from the algorithm's output reported a strong perception of depth. PMID:16519351
Pressure Calculation in a Compressor Cylinder by a Modified New Helmholtz Modelling
NASA Astrophysics Data System (ADS)
MA, Y.-C.; MIN, O.-K.
2001-06-01
Pressure pulsation has a critical importance in the design of refrigerant compressor since it affects the performance by increasing over-compression loss, and it acts as a noise and vibration source. For the numerical analysis of pressure pulsation, quasi-steady flow equation has been used because of its easy manipulation derived from the pressure difference. By considering the dynamic effects of fluid, a new Helmholtz resonator model was also proposed on the basis of the continuity and the momentum equations, which consists of necks and cavities in flow manifolds.In this paper, a modified new Helmholtz resonator is introduced to include the gas inertia effect due to the volume decrease in the cavity. Comparisons between this modified new Helmholtz calculations and experimental results show that it is necessary to include the gas inertia effect in predicting pressure over-shooting phenomena at an instant of valve opening state and this modified new Helmholtz model can describe the over-compression phenomena in the compressor cylinder, a phenomenon which hinders a noise source identification of compressor.
MT3D was first developed by Chunmiao Zheng in 1990 at S.S. Papadopulos & Associates, Inc. with partial support from the U.S. Environmental Protection Agency (USEPA). Starting in 1990, MT3D was released as a pubic domain code from the USEPA. Commercial versions with enhanced capab...
NASA Technical Reports Server (NTRS)
1977-01-01
A market study of a proposed version of a 3-D eyetracker for initial use at NASA's Ames Research Center was made. The commercialization potential of a simplified, less expensive 3-D eyetracker was ascertained. Primary focus on present and potential users of eyetrackers, as well as present and potential manufacturers has provided an effective means of analyzing the prospects for commercialization.
Energy Science and Technology Software Center (ESTSC)
2013-10-01
Earth3D is a computer code designed to allow fast calculation of seismic rays and travel times through a 3D model of the Earth. LLNL is using this for earthquake location and global tomography efforts and such codes are of great interest to the Earth Science community.
[3-D ultrasound in gastroenterology].
Zoller, W G; Liess, H
1994-06-01
Three-dimensional (3D) sonography represents a development of noninvasive diagnostic imaging by real-time two-dimensional (2D) sonography. The use of transparent rotating scans, comparable to a block of glass, generates a 3D effect. The objective of the present study was to optimate 3D presentation of abdominal findings. Additional investigations were made with a new volumetric program to determine the volume of selected findings of the liver. The results were compared with the estimated volumes of 2D sonography and 2D computer tomography (CT). For the processing of 3D images, typical parameter constellations were found for the different findings, which facilitated processing of 3D images. In more than 75% of the cases examined we found an optimal 3D presentation of sonographic findings with respect to the evaluation criteria developed by us for the 3D imaging of processed data. Great differences were found for the estimated volumes of the findings of the liver concerning the three different techniques applied. 3D ultrasound represents a valuable method to judge morphological appearance in abdominal findings. The possibility of volumetric measurements enlarges its potential diagnostic significance. Further clinical investigations are necessary to find out if definite differentiation between benign and malign findings is possible. PMID:7919882
2013-10-30
This video provides an overview of the Sandia National Laboratories developed 3-D World Model Building capability that provides users with an immersive, texture rich 3-D model of their environment in minutes using a laptop and color and depth camera.
None
2014-02-26
This video provides an overview of the Sandia National Laboratories developed 3-D World Model Building capability that provides users with an immersive, texture rich 3-D model of their environment in minutes using a laptop and color and depth camera.
NASA Astrophysics Data System (ADS)
Walsh, J. R.
2004-02-01
The Euro3D RTN is an EU funded Research Training Network to foster the exploitation of 3D spectroscopy in Europe. 3D spectroscopy is a general term for spectroscopy of an area of the sky and derives its name from its two spatial + one spectral dimensions. There are an increasing number of instruments which use integral field devices to achieve spectroscopy of an area of the sky, either using lens arrays, optical fibres or image slicers, to pack spectra of multiple pixels on the sky (``spaxels'') onto a 2D detector. On account of the large volume of data and the special methods required to reduce and analyse 3D data, there are only a few centres of expertise and these are mostly involved with instrument developments. There is a perceived lack of expertise in 3D spectroscopy spread though the astronomical community and its use in the armoury of the observational astronomer is viewed as being highly specialised. For precisely this reason the Euro3D RTN was proposed to train young researchers in this area and develop user tools to widen the experience with this particular type of data in Europe. The Euro3D RTN is coordinated by Martin M. Roth (Astrophysikalisches Institut Potsdam) and has been running since July 2002. The first Euro3D science conference was held in Cambridge, UK from 22 to 23 May 2003. The main emphasis of the conference was, in keeping with the RTN, to expose the work of the young post-docs who are funded by the RTN. In addition the team members from the eleven European institutes involved in Euro3D also presented instrumental and observational developments. The conference was organized by Andy Bunker and held at the Institute of Astronomy. There were over thirty participants and 26 talks covered the whole range of application of 3D techniques. The science ranged from Galactic planetary nebulae and globular clusters to kinematics of nearby galaxies out to objects at high redshift. Several talks were devoted to reporting recent observations with newly
NASA Technical Reports Server (NTRS)
Walatka, Pamela P.; Buning, Pieter G.; Pierce, Larry; Elson, Patricia A.
1990-01-01
PLOT3D is a computer graphics program designed to visualize the grids and solutions of computational fluid dynamics. Seventy-four functions are available. Versions are available for many systems. PLOT3D can handle multiple grids with a million or more grid points, and can produce varieties of model renderings, such as wireframe or flat shaded. Output from PLOT3D can be used in animation programs. The first part of this manual is a tutorial that takes the reader, keystroke by keystroke, through a PLOT3D session. The second part of the manual contains reference chapters, including the helpfile, data file formats, advice on changing PLOT3D, and sample command files.
Dawood, A; Marti Marti, B; Sauret-Jackson, V; Darwood, A
2015-12-01
3D printing has been hailed as a disruptive technology which will change manufacturing. Used in aerospace, defence, art and design, 3D printing is becoming a subject of great interest in surgery. The technology has a particular resonance with dentistry, and with advances in 3D imaging and modelling technologies such as cone beam computed tomography and intraoral scanning, and with the relatively long history of the use of CAD CAM technologies in dentistry, it will become of increasing importance. Uses of 3D printing include the production of drill guides for dental implants, the production of physical models for prosthodontics, orthodontics and surgery, the manufacture of dental, craniomaxillofacial and orthopaedic implants, and the fabrication of copings and frameworks for implant and dental restorations. This paper reviews the types of 3D printing technologies available and their various applications in dentistry and in maxillofacial surgery. PMID:26657435
Hermann von Helmholtz and his students
NASA Astrophysics Data System (ADS)
Mulligan, Joseph F.
1989-01-01
During the years 1871-1888, when Hermann von Helmholtz was professor of physics at the University of Berlin, physicists from all over the world flocked to Berlin to study and do research with him. Among these were the German physicists Max Planck, Heinrich Kayser, Eugen Goldstein, Wilhelm Wien, and Heinrich Hertz, and Americans Henry Rowland, A. A. Michelson, and Michael Pupin. Examples of Helmholtz's scientific and personal interactions with these students and research associates show why he is justly considered the outstanding physics mentor of the 19th century. Both his ideas and his students played a major role in the development of physics in the late 19th and early 20th centuries.
Stanton, M M; Samitier, J; Sánchez, S
2015-08-01
Three-dimensional (3D) bioprinting has recently emerged as an extension of 3D material printing, by using biocompatible or cellular components to build structures in an additive, layer-by-layer methodology for encapsulation and culture of cells. These 3D systems allow for cell culture in a suspension for formation of highly organized tissue or controlled spatial orientation of cell environments. The in vitro 3D cellular environments simulate the complexity of an in vivo environment and natural extracellular matrices (ECM). This paper will focus on bioprinting utilizing hydrogels as 3D scaffolds. Hydrogels are advantageous for cell culture as they are highly permeable to cell culture media, nutrients, and waste products generated during metabolic cell processes. They have the ability to be fabricated in customized shapes with various material properties with dimensions at the micron scale. 3D hydrogels are a reliable method for biocompatible 3D printing and have applications in tissue engineering, drug screening, and organ on a chip models. PMID:26066320
Unassisted 3D camera calibration
NASA Astrophysics Data System (ADS)
Atanassov, Kalin; Ramachandra, Vikas; Nash, James; Goma, Sergio R.
2012-03-01
With the rapid growth of 3D technology, 3D image capture has become a critical part of the 3D feature set on mobile phones. 3D image quality is affected by the scene geometry as well as on-the-device processing. An automatic 3D system usually assumes known camera poses accomplished by factory calibration using a special chart. In real life settings, pose parameters estimated by factory calibration can be negatively impacted by movements of the lens barrel due to shaking, focusing, or camera drop. If any of these factors displaces the optical axes of either or both cameras, vertical disparity might exceed the maximum tolerable margin and the 3D user may experience eye strain or headaches. To make 3D capture more practical, one needs to consider unassisted (on arbitrary scenes) calibration. In this paper, we propose an algorithm that relies on detection and matching of keypoints between left and right images. Frames containing erroneous matches, along with frames with insufficiently rich keypoint constellations, are detected and discarded. Roll, pitch yaw , and scale differences between left and right frames are then estimated. The algorithm performance is evaluated in terms of the remaining vertical disparity as compared to the maximum tolerable vertical disparity.
Arena3D: visualization of biological networks in 3D
Pavlopoulos, Georgios A; O'Donoghue, Seán I; Satagopam, Venkata P; Soldatos, Theodoros G; Pafilis, Evangelos; Schneider, Reinhard
2008-01-01
Background Complexity is a key problem when visualizing biological networks; as the number of entities increases, most graphical views become incomprehensible. Our goal is to enable many thousands of entities to be visualized meaningfully and with high performance. Results We present a new visualization tool, Arena3D, which introduces a new concept of staggered layers in 3D space. Related data – such as proteins, chemicals, or pathways – can be grouped onto separate layers and arranged via layout algorithms, such as Fruchterman-Reingold, distance geometry, and a novel hierarchical layout. Data on a layer can be clustered via k-means, affinity propagation, Markov clustering, neighbor joining, tree clustering, or UPGMA ('unweighted pair-group method with arithmetic mean'). A simple input format defines the name and URL for each node, and defines connections or similarity scores between pairs of nodes. The use of Arena3D is illustrated with datasets related to Huntington's disease. Conclusion Arena3D is a user friendly visualization tool that is able to visualize biological or any other network in 3D space. It is free for academic use and runs on any platform. It can be downloaded or lunched directly from . Java3D library and Java 1.5 need to be pre-installed for the software to run. PMID:19040715
NASA Astrophysics Data System (ADS)
Otis, Collin; Ferrero, Pietro; Candler, Graham; Givi, Peyman
2013-11-01
The scalar filtered mass density function (SFMDF) methodology is implemented into the computer code US3D. This is an unstructured Eulerian finite volume hydrodynamic solver and has proven very effective for simulation of compressible turbulent flows. The resulting SFMDF-US3D code is employed for large eddy simulation (LES) on unstructured meshes. Simulations are conducted of subsonic and supersonic flows under non-reacting and reacting conditions. The consistency and the accuracy of the simulated results are assessed along with appraisal of the overall performance of the methodology. The SFMDF-US3D is now capable of simulating high speed flows in complex configurations.
Kelvin Helmholtz Instability in Planetary Magnetospheres
NASA Astrophysics Data System (ADS)
Johnson, Jay R.; Wing, Simon; Delamere, Peter A.
2014-11-01
Kelvin-Helmholtz instability plays a particularly important role in plasma transport at magnetospheric boundaries because it can control the development of a turbulent boundary layer, which governs the transport of mass, momentum, and energy across the boundary. Waves generated at the interface can also couple into body modes in the plasma sheet and inner magnetosphere where they can play an important role in plasma sheet transport and particle energization in the inner magnetosphere. Kinetic and electron-scale effects are important for the development of K-H instability, leading to secondary instabilities and plasma mixing. The development of vortices that entwine magnetosheath field lines with magnetospheric field lines also allows reconnection and the interchange of plasma blobs from open to closed field lines. Dawn-dusk asymmetries in Kelvin-Helmholtz development at planetary boundary layers may result from several effects including plasma corotation, kinetic effects, magnetic geometry, or asymmetric distribution of plasma. Examples are provided throughout the solar system illustrating the pervasive effects of the Kelvin-Helmholtz instability on plasma transport.
3D Inverse problem: Seawater intrusions
NASA Astrophysics Data System (ADS)
Steklova, K.; Haber, E.
2013-12-01
Modeling of seawater intrusions (SWI) is challenging as it involves solving the governing equations for variable density flow, multiple time scales and varying boundary conditions. Due to the nonlinearity of the equations and the large aquifer domains, 3D computations are a costly process, particularly when solving the inverse SWI problem. In addition the heads and concentration measurements are difficult to obtain due to mixing, saline wedge location is sensitive to aquifer topography, and there is general uncertainty in initial and boundary conditions and parameters. Some of these complications can be overcome by using indirect geophysical data next to standard groundwater measurements, however, the inverse problem is usually simplified, e.g. by zonation for the parameters based on geological information, steady state substitution of the unknown initial conditions, decoupling the equations or reducing the amount of unknown parameters by covariance analysis. In our work we present a discretization of the flow and solute mass balance equations for variable groundwater (GW) flow. A finite difference scheme is to solve pressure equation and a Semi - Lagrangian method for solute transport equation. In this way we are able to choose an arbitrarily large time step without losing stability up to an accuracy requirement coming from the coupled character of the variable density flow equations. We derive analytical sensitivities of the GW model for parameters related to the porous media properties and also the initial solute distribution. Analytically derived sensitivities reduce the computational cost of inverse problem, but also give insight for maximizing information in collected data. If the geophysical data are available it also enables simultaneous calibration in a coupled hydrogeophysical framework. The 3D inverse problem was tested on artificial time dependent data for pressure and solute content coming from a GW forward model and/or geophysical forward model. Two