Three‐dimensional acoustic modeling by the Fourier method

Geophysics ◽  
1988 ◽  
Vol 53 (9) ◽  
pp. 1175-1183 ◽  
Author(s):  
Moshe Reshef ◽  
Dan Kosloff ◽  
Mickey Edwards ◽  
Chris Hsiung
Keyword(s):  
Three Dimensional ◽  
Fourier Method ◽  
Forward Modeling ◽  
Secondary Memory ◽  
Storage Device ◽  
Data Sets ◽  
Time Step ◽  
Absorbing Boundary ◽  
Time Stepping ◽  
Spatial Grid

A three‐dimensional forward modeling algorithm, allowing arbitrary density and arbitrary wave propagation velocity in lateral and vertical directions, directly solves the acoustic wave equation through spatial and temporal discretization. Spatial partial differentiation is performed in the Fourier domain. Time stepping is performed with a second‐order differencing operator. Modeling includes an optional free surface above the spatial grid. An absorbing boundary is applied on the lateral and bottom edges of the spatial grid. Three‐dimensional forward modeling represents a challenge for computer technology. Computation of meaningfully sized models requires extensive calculations and large three‐dimensional data sets which must be retrieved and restored during the computation of each time step. The computational feasibility of the Fourier method is demonstrated by implementation on the multiprocessor CRAY X‐MP computer system using the large secondary memory of the solid‐state storage device (SSD). Calculations use vectorization and parallel processing architecture. The similarity of numerical and analytical results indicates sufficient accuracy for many applications.

Numerical Solution of Incompressible Unsteady Flows in Turbomachinery

2000 ◽  
Vol 123 (3) ◽  
pp. 680-685 ◽  
Author(s):  
L. He ◽  
K. Sato
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Time Stepping ◽  
Incompressible Viscous Flow ◽  
Dual Time Stepping

A three-dimensional incompressible viscous flow solver of the thin-layer Navier-Stokes equations was developed for the unsteady turbomachinery flow computations. The solution algorithm for the unsteady flows combines the dual time stepping technique with the artificial compressibility approach for solving the incompressible unsteady flow governing equations. For time accurate calculations, subiterations are introduced by marching the equations in the pseudo-time to fully recover the incompressible continuity equation at each real time step, accelerated with a multi-grid technique. Computations of test cases show satisfactory agreements with corresponding theoretical and experimental results, demonstrating the validity and applicability of the present method to unsteady incompressible turbomachinery flows.

Three‐dimensional elastic modeling by the Fourier method

Geophysics ◽  
1988 ◽  
Vol 53 (9) ◽  
pp. 1184-1193 ◽  
Author(s):  
Moshe Reshef ◽  
Dan Kosloff ◽  
Mickey Edwards ◽  
Chris Hsiung
Keyword(s):  
Wave Velocity ◽  
Three Dimensional ◽  
P Wave ◽  
Velocity Variation ◽  
Difference Operators ◽  
Time Step ◽  
Current Time ◽  
Partial Differentiation ◽  
Wide Range ◽  
Spatial Grid

Earlier work on three‐dimensional forward modeling is extended to elastic waves using the equations of conservation of momentum and the stress‐strain relations for an isotropic elastic medium undergoing infinitesimal deformation. In addition to arbitrary compressional (or P‐wave) velocity and density variation in lateral and vertical directions, elastic modeling permits shear (or S‐wave) velocity variation as well. The elastic wave equation is solved using a generalization of the method for the acoustic case. Computation of each time step begins by computing six strain components by performing nine spatial partial differentiation operations on the three displacement components from the previous time step. The six strains and two Lamé constants are linearly combined to yield six stress components. Nine spatial partial differentiation operations on the six stresses, three body forces, and density are used to compute second partial time derivatives of the three displacement components. Time stepping to obtain the three displacement components for the current time step is performed with second‐order difference operators. The modeling includes an optional free surface above the spatial grid. An absorbing boundary is applied on the lateral and bottom edges of the spatial grid. This modeling scheme is implemented on a four‐processor CRAY X‐MP computer system using the solid‐state storage device (SSD). Using parallel processing with four CPUs, a reasonable geologic model can be computed within a few hours. The modeling scheme provides a variety of seismic source types and many possible output displays. These features enable the modeling of a wide range of seismic surveys. Numerical and analytic results are presented.

On Direct and Semi-Direct Inverse of Stokes, Helmholtz and Laplacian Operators in View of Time-Stepper-Based Newton and Arnoldi Solvers in Incompressible CFD

2013 ◽  
Vol 14 (4) ◽  
pp. 1103-1119 ◽  
Author(s):  
H. Vitoshkin ◽  
A. Yu. Gelfgat
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Computational Effort ◽  
Stokes Operator ◽  
Time Step ◽  
Time Stepping ◽  
Fast Direct Solvers ◽  
Large Time Step ◽  
Helmholtz Operators ◽  
Laplacian Operators

AbstractFactorization of the incompressible Stokes operator linking pressure and velocity is revisited. The main purpose is to use the inverse of the Stokes operator with a large time step as a preconditioner for Newton and Arnoldi iterations applied to computation of steady three-dimensional flows and study of their stability. It is shown that the Stokes operator can be inversed within an acceptable computational effort. This inverse includes fast direct inverses of several Helmholtz operators and iterative inverse of the pressure matrix. It is shown, additionally, that fast direct solvers can be attractive for the inverse of the Helmholtz and Laplace operators on fine grids and at large Reynolds numbers, as well as for other problems where convergence of iterative methods slows down. Implementation of the Stokes operator inverse to time-stepping-based formulation of the Newton and Arnoldi iterations is discussed.

Time step n-tupling for wave equations

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. T249-T254 ◽  
Author(s):  
Lasse Amundsen ◽  
Ørjan Pedersen
Keyword(s):  
Discrete Time ◽  
Wave Equations ◽  
Fourier Method ◽  
Computational Effort ◽  
Second Order ◽  
Time Step ◽  
Time Stepping ◽  
Previous Time ◽  
Time Integrators ◽  
New Time

We have constructed novel temporal discretizations for wave equations. We first select an explicit time integrator that is of second order, leading to classic time marching schemes in which the next value of the wavefield at the discrete time [Formula: see text] is computed from current values known at time [Formula: see text] and the previous time [Formula: see text]. Then, we determine how the time step can be doubled, tripled, or generally, [Formula: see text]-tupled, producing a new time-stepping method in which the next value of the wavefield at the discrete time [Formula: see text] is computed from current values known at time [Formula: see text] and the previous time [Formula: see text]. In-between time values of the wavefield are eliminated. Using the Fourier method to calculate space derivatives, the new time integrators allow larger stable time steps than traditional time integrators; however, like the Lax-Wendroff procedure, they require more computational effort per time step. Because the new schemes are developed from the classic second-order time-stepping scheme, they will have the same properties, except the Courant-Friedrichs-Lewy stability condition, which becomes relaxed by the factor [Formula: see text] compared with the classic scheme. As an example, we determine the method for solving scalar wave propagation in which doubling the time step is 15% faster than a Lax-Wendroff correction scheme of the same spatial order because it can increase the time step by [Formula: see text] only.

Forward modeling by a Fourier method

Geophysics ◽  
1982 ◽  
Vol 47 (10) ◽  
pp. 1402-1412 ◽  
Author(s):  
Dan D. Kosloff ◽  
Edip Baysal
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Physical Model ◽  
Finite Difference Methods ◽  
Three Dimensional ◽  
Fourier Method ◽  
Single Layer ◽  
Forward Modeling ◽  
Difference Methods ◽  
Grid Points

A Fourier or pseudospectral forward‐modeling algorithm for solving the two‐dimensional acoustic wave equation is presented. The method utilizes a spatial numerical grid to calculate spatial derivatives by the fast Fourier transform. Time derivatives which appear in the wave equation are calculated by second‐order differencing. The scheme requires fewer grid points than finite‐difference methods to achieve the same accuracy. It is therefore believed that the Fourier method will prove more efficient than finite‐difference methods, especially when dealing with three‐dimensional models. The Fourier forward‐modeling method was tested against two problems, a single‐layer problem with a known analytic solution and a wedge problem which was also tested by physical modeling. The numerical results agreed with both the analytic and physical model results. Furthermore, the numerical model facilitates the explanation of certain events on the time section of the physical model which otherwise could not easily be taken into account.

Computer-aided methods for 3-D visualization of serial sections and thick biological specimens

1992 ◽  
Vol 50 (2) ◽  
pp. 1060-1061
Author(s):  
Mark Ellisman ◽  
Maryann Martone ◽  
Gabriel Soto ◽  
Eleizer Masliah ◽  
David Hessler ◽  
...  
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Three Dimensional ◽  
Neuritic Plaque ◽  
Dimensional Structure ◽  
Data Sets ◽  
Molecular Physiology ◽  
Research Activities ◽  
Computer Aided ◽  
Dimensional Reconstruction

Structurally-oriented biologists examine cells, tissues, organelles and macromolecules in order to gain insight into cellular and molecular physiology by relating structure to function. The understanding of these structures can be greatly enhanced by the use of techniques for the visualization and quantitative analysis of three-dimensional structure. Three projects from current research activities will be presented in order to illustrate both the present capabilities of computer aided techniques as well as their limitations and future possibilities.The first project concerns the three-dimensional reconstruction of the neuritic plaques found in the brains of patients with Alzheimer's disease. We have developed a software package “Synu” for investigation of 3D data sets which has been used in conjunction with laser confocal light microscopy to study the structure of the neuritic plaque. Tissue sections of autopsy samples from patients with Alzheimer's disease were double-labeled for tau, a cytoskeletal marker for abnormal neurites, and synaptophysin, a marker of presynaptic terminals.

scholarly journals Elastic transformation of histological slices allows precise co-registration with microCT data sets for a refined virtual histology approach

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jonas Albers ◽  
Angelika Svetlove ◽  
Justus Alves ◽  
Alexander Kraupner ◽  
Francesca di Lillo ◽  
...  
Keyword(s):  
Three Dimensional ◽  
High Specificity ◽  
Histopathological Analysis ◽  
Specific Information ◽  
Data Sets ◽  
Virtual Histology ◽  
Novel Approach ◽  
Cell Tissue ◽  
Immuno Histochemistry ◽  
3D Information

AbstractAlthough X-ray based 3D virtual histology is an emerging tool for the analysis of biological tissue, it falls short in terms of specificity when compared to conventional histology. Thus, the aim was to establish a novel approach that combines 3D information provided by microCT with high specificity that only (immuno-)histochemistry can offer. For this purpose, we developed a software frontend, which utilises an elastic transformation technique to accurately co-register various histological and immunohistochemical stainings with free propagation phase contrast synchrotron radiation microCT. We demonstrate that the precision of the overlay of both imaging modalities is significantly improved by performing our elastic registration workflow, as evidenced by calculation of the displacement index. To illustrate the need for an elastic co-registration approach we examined specimens from a mouse model of breast cancer with injected metal-based nanoparticles. Using the elastic transformation pipeline, we were able to co-localise the nanoparticles to specifically stained cells or tissue structures into their three-dimensional anatomical context. Additionally, we performed a semi-automated tissue structure and cell classification. This workflow provides new insights on histopathological analysis by combining CT specific three-dimensional information with cell/tissue specific information provided by classical histology.

scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

scholarly journals Validation of Scolioscan Air-Portable Radiation-Free Three-Dimensional Ultrasound Imaging Assessment System for Scoliosis

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2858
Author(s):  
Kelly Ka-Lee Lai ◽  
Timothy Tin-Yan Lee ◽  
Michael Ka-Shing Lee ◽  
Joseph Chi-Ho Hui ◽  
Yong-Ping Zheng
Keyword(s):  
Ultrasound Imaging ◽  
Imaging System ◽  
Outcome Measurement ◽  
Three Dimensional ◽  
3D Ultrasound ◽  
Mean Difference ◽  
Assessment System ◽  
Absolute Difference ◽  
Data Sets ◽  
Low Profile

To diagnose scoliosis, the standing radiograph with Cobb’s method is the gold standard for clinical practice. Recently, three-dimensional (3D) ultrasound imaging, which is radiation-free and inexpensive, has been demonstrated to be reliable for the assessment of scoliosis and validated by several groups. A portable 3D ultrasound system for scoliosis assessment is very much demanded, as it can further extend its potential applications for scoliosis screening, diagnosis, monitoring, treatment outcome measurement, and progress prediction. The aim of this study was to investigate the reliability of a newly developed portable 3D ultrasound imaging system, Scolioscan Air, for scoliosis assessment using coronal images it generated. The system was comprised of a handheld probe and tablet PC linking with a USB cable, and the probe further included a palm-sized ultrasound module together with a low-profile optical spatial sensor. A plastic phantom with three different angle structures built-in was used to evaluate the accuracy of measurement by positioning in 10 different orientations. Then, 19 volunteers with scoliosis (13F and 6M; Age: 13.6 ± 3.2 years) with different severity of scoliosis were assessed. Each subject underwent scanning by a commercially available 3D ultrasound imaging system, Scolioscan, and the portable 3D ultrasound imaging system, with the same posture on the same date. The spinal process angles (SPA) were measured in the coronal images formed by both systems and compared with each other. The angle phantom measurement showed the measured angles well agreed with the designed values, 59.7 ± 2.9 vs. 60 degrees, 40.8 ± 1.9 vs. 40 degrees, and 20.9 ± 2.1 vs. 20 degrees. For the subject tests, results demonstrated that there was a very good agreement between the angles obtained by the two systems, with a strong correlation (R2 = 0.78) for the 29 curves measured. The absolute difference between the two data sets was 2.9 ± 1.8 degrees. In addition, there was a small mean difference of 1.2 degrees, and the differences were symmetrically distributed around the mean difference according to the Bland–Altman test. Scolioscan Air was sufficiently comparable to Scolioscan in scoliosis assessment, overcoming the space limitation of Scolioscan and thus providing wider applications. Further studies involving a larger number of subjects are worthwhile to demonstrate its potential clinical values for the management of scoliosis.

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