FD Method Research Articles

Scattering analysis of large‐scale cavities using the nonstandard FDTD method

AbstractThe nonstandard FDTD method has been proposed for highly accurate numerical analysis of large structures. However, the conventional nonstandard FDTD has been defined only with isotropic grids, and hence the treatment of arbitrary cavity shapes has been severely restricted. In order to remove this restriction in this paper, the nonstandard FDTD method is extended to more general noniso‐tropic grids. First, the FD Laplacian for the nonisotropic grids is newly defined. From the expression for decomposition by the first‐order difference operator, the nonstandard FDTD equations are derived for nonisotropic grids. The physical meaning of the nonstandard FD method used in the nonstandard FDTD method is clarified. Next, by means of the nonstandard FDTD method extended to nonisotropic grids, a scattering analysis of large‐scale cavities is performed and its effectiveness is demonstrated. The results obtained by the nonstandard FDTD method agree well with the measured values, confirming that the nonstandard FDTD method is effective as a highly accurate scattering analysis method for large‐scale cavities. © 2001 Scripta Technica, Electron Comm Jpn Pt 2, 84(12): 8–16, 2001

From unstable to stable seismic modelling by finite-difference method

FD modelling of the two-dimensional P-SV seismic response is performed for the Volvi Lake sedimentary basin at EURO-SEISTEST site. The basin is 6 km long and 200 m deep. Viscoelastic linear rheology, with the attenuation described by Q proportional to frequency is used. The FD synthetics are accurate up to 4.6Hz. This means 10 gridpoints per shortest S-wavelength corresponding to frequency of 4.6Hz. The site is characterized by complex structure, with high velocity contrasts between individual blocks, (vS = 2600 m/s)/(vS = 425 m/s); also the vpvs velocity ratio is up to 5. Numeric instabilities have been found at contacts between blocks with high and low vpvs ratios. A simple trick to stabilize the calculations for long FD runs (e.g. 20 000 time levels, or more) has been suggested. It consists of a special algorithmic treatment of the material discontinuities, preventing mixing of very large and very small values of the so-called effective material parameters within a grid cell. Appendix provides a comparison of the present FD method with an independent method for a model with non-planar topography and several vPvs ratios.

Design of inhalation dry powder of pranlukast hydrate to improve dispersibility by the surface modification with light anhydrous silicic acid (AEROSIL 200)

A new particle design method was proposed for dry powder inhalation of hydrophobic cohesive drug particles (pranlukast hydrate, D 50=2.1 μm) by the surface modification with hydrophilic colloidal silica (AEROSIL, D 50=16 nm). The surface of drug particle was modified by compounding AEROSIL (2–10%) under shear with a manually operating mortar (PM method) or a high-speed elliptical-rotor-type mixer (Theta-Composer ®, TC method). The surface modifications were also conducted by lyophilizing (FD method) or spray drying (SD method) the aqueous dispersions of the drug and AEROSIL. The surface modified particles were aerosolized through a Spinhaler ® and their inhalation behaviors were evaluated by a twin impinger in vitro. The inhalation behaviors were evaluated by the coefficient of inhalation efficiency (EI) defined as the geometric mean of the drug % emitted from the device and delivered % in respirable fraction of the twin impinger. The EI of modified particles with TC, FD and SD methods were dramatically increased up to 66.9, 52.7 and 47.7%, respectively, with increasing AEROSIL content compared with that of (22.4%) original powder. The surface modification to hydrophilic with AEROSIL reduced the cohesive force between the drug particles, owing to the decrease in van der Waals and electrostatic forces, improving the dispersibilities of emitted particles from the Spinhaler ®.

Characterization of a magnetoplasma integrated channel waveguide using FD–FD method

Characterization of a magnetoplasma integrated channel waveguide using FD–FD method

Characterization of a magnetoplasma integrated channel waveguide using FD–FD method

The finite-difference in the frequency-domain (FD–FD) method is used here to study the propagation characteristics of an integrated channel waveguide, consisting of a plasma controlled by a magnetostatic field (magnetoplasma). The dependence relation between resonance and cyclotron frequency, collision frequency, channel dimensions, and plasma frequency is shown. The formulation is developed in terms of the transverse magnetic field components such that the problem is transformed into a conventional eigenvalue problem. The elimination of the spurious modes is obtained with the implicit inclusion of ∇⋅B=0. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 19: 38–42, 1998.

Comparison of the perturbative convergence with multireference Möller–Plesset, Epstein–Nesbet, forced degenerate and optimized zeroth order partitionings: The excited BeH2 surface

High order perturbation energies are computed for excited 1A1 states of BeH2 at geometries near the Be→H2 symmetric insertion transition state. The equations of multireference perturbation theory are solved through 30th order to study the difficulties in selecting the appropriate zeroth order Hamiltonian, orbitals, orbital energies, and reference functions for the computations of smooth molecular potential energy surfaces. The origin of the perturbative divergence produced by Möller–Plesset and Epstein–Nesbet partitionings is analyzed using a conceptually simple two-state model constructed using one state each from the reference and orthogonal spaces. The optimized zeroth order partitioning scheme (OPT) for double reference space computations with configurations 1a122a123a12 and 1a122a121b22 produces a truly convergent perturbation expansion through 30th order. The OPT energies are accurate in low orders as compared to the exact (197 dimensional) solution within the basis. The forced valence orbital degeneracy partitioning method (FD) also generates a truly convergent expansion for the same double reference space calculation, with slightly poorer low order energies than the OPT scheme. The BeH2 system facilitates the consideration of larger reference spaces (constructed using three through six orbitals) where the FD method produces highly accurate energies in low orders despite the asymptotic nature of the FD perturbation expansion. The “delayed’’ perturbative divergence behavior with the FD partitioning scheme (for large reference spaces) is shown to occur due to the incorrect ordering between the zeroth order energies of some reference and complementary space levels.

A local mesh refinement algorithm for the FDFD method using a polygonal grid

A local mesh refinement algorithm for the finite-difference method in the frequency domain (FDFD) is presented that is based on polygonal grids. It is applied to a simple test structure for which the propagation parameters were computed with a mode-matching method as a reference. It is shown that the local mesh refinement realized with this polygonal grid significantly improves the accuracy of the propagation constant compared to the conventional FD method based on rectangular meshes.

The FD method for first-order linear hyperbolic differential equations with piecewise smooth coefficients

A justification of the differential-discrete FD method for solving one class of first-order linear partial differential equations with piecewise smooth coefficients, a right-hand side, and initial conditions is presented. The convergence rate of the method is shown to be limited exclusively by the smoothness of the input information. High accuracy, ease of algorithmic implementation, and feasibility of representation of results in an analytical form point to the advantage of the FD method over the other methods for the given class of problems. Bibliography:6 titles.

FD method of arbitrary uniform order of accuracy for solving singularly perturbed boundary problems for second-order ordinary differential equations

Using a functional-discrete approach, three-point difference schemes of arbitrary order of accuracy are constructed for solving the Dirichlet problem for second-order ordinary differential equations (ODE) with a small parameter multiplying the leading derivative. The uniform convergence of the schemes with respect to the small parameter is proved, and a recursive algorithm for their realization is constructed. Bibliography:4 titles.

NUMERICAL SIMULATION OF HIGH SPEED INDUCTION MACHINE WITH SOLID ROTOR

In this paper the calculation method of High Speed Induction Machine with solid rotor is presented. 2D model is assumed. FD method is used. Nonlinear effect of permeability is take into account.

Seismic wave propagation in complex crust-upper mantle media using 2-D finite-difference synthetics

SUMMARY A description is given of the numerical FD scheme used to solve the elasti wave equation, including a few remarks on the source functions used. Our FD method has been used for computing synthetic seismograms for 2-D crust/upper mantle models of size 150 × 400 km2, with options for free-surface topography. The strategy was to introduce successively more complex lithosphere models for generating the synthetics; the reference model was laterally homogeneous lithosphere. The interface scattering was visualized through displays of free-surface synthetic waveforms and snapshots for models with a corrugated Moho only and free surface topography only. Near the free surface the latter seems to dominate, in the form of P-to-Rg and S-to-Rg conversions. Lithosphere randomizations were introduced through von Karman functions of order n= 0.3, with rms velocity fluctuations of 3–4 per cent and correlation distances (horizontal and vertical) at 2.5 or 10 km. In case of a medium with only sub-Moho heterogeneities, those with horizontal anisotropy (ax= 10 km; az= 2.5 km) produced relatively strong Pn and Sn phases. The respective codas were dominated as in most of our experiments by P-to-S and S-to-S scattering wavelets excluding Rg scattering at a free surface with topography. For a medium with crustal heterogeneities, the distortions of the P and S wave trains with distance were clearly demonstrated. For full-scale heterogeneous lithosphere models, characteristic features of the synthetics were quantitatively similar to observational records of local events. Dominant attributes were a pronounced P coda consisting mainly of P- and Rg-scattered wavelets, and a relatively strong S coda consisting mainly of P-to-S and S-to-S scattered wavelets. The P and S waveforms are severely distorted pointing at the futility of reliably picking many secondary arrivals in local event recordings. Most of the scattering wavelets are confined to the crustal waveguide and to surface waves, since coda excitations for sensors at a depth of 100 km were weak and, moreover, consisted mainly of S wavelets. This implies that a strong teleseismic P coda does not reflect scattering within the crust in the source region but, rather, a complex source. Observational results from analysis of NORESS and ARCESS local event recordings are also presented. Clearly the lithosphere is not isotropically inhomogeneous. The essence of our 2-D FD synthetic seismogram experiments is that a simple lithosphere model, being moderately heterogeneous, gives rise to complex seismograms which are grossly similar to the observational recordings. In contrast, complex models derived from profiling surveys (but lacking the fine-scale random variations) give simple,‘ray tracing’like synthetics, not necessarily similar to the observed records.

A Comparison of Methods for Estimating a Transfer Function.

Three methods for estimating a transfer function of a system with two inputs were compared. The first is a method based on the analysis in frequency domain (FD method). The second method makes use of the autoregressive model (AR method). The third one uses the multiple regression model (MR method). These methods were applied to 100 pairs of artificial data which were synthesized on the basis of three kinds of assumed transfer functions. It is concluded from the results of comparison that MR method is the best of the three.

Numerical modeling of the flow discharge in MPD thrusters

Two theoretical models for calculating the current and flow distributions in self-field MPD thrusters have been developed and are applied to evaluate the effects of geometry, propellant type, scaling, and other parameters on the thruster performance. For continuous thrusters, a stationary code has been developed. The extended Ohm's law is used to calculate the current contour lines, and a one-dimensional, two-component expansion flow model is applied to obtain the velocity, temperature, and pressure distributions for calculating the gas properties, which are again used in Ohm's law. An integration over the volume and thermal forces equals the thrust. The differential equation is solved by means of a finite-difference method for the geometry of the nozzle-type plasma thruster DT2-IRS, which has been investigated experimentally in a steady-state as well as in a quasi-steady-state mode. The calculated current density distribution and the computed thrust are compared with these experimental results. For the starting phase of the steady-state MPD thrusters as well as for pulsed thrusters, a time-dependent, fully two-dimensional code has been developed. It uses a modified McCormack FD method in cylindrical coordinates to calculate the time-dependent flow, temperature, and pressure fields.

Pharmacokinetics and comparative nephrotoxicity of fixed-dose versus fixed-interval reduction of gentamicin dosage in subtotal nephrectomized dogs

There is presently no consensus as to the relative safety of fixed-interval/reduced dose (FI) vs fixed-dose/increased interval (FD) dosage adjustment regiments for use in renal insufficiency. This study compared their nephrotoxic potential using gentamicin in beagle dogs with renal insufficiency secondary to subtotal surgical nephrectomy. Pharmacokinetic analysis in six dogs showed that this surgical procedure resulted in a decreased total body clearance of drug and a marginally contracted volume of the central compartment. An allometric analysis of gentamicin disposition in different species was used to derive a human-equivalent maximum canine nontoxic dose of 9 mg kg −1 day −1. Nephrotoxicity was detected by histopathologic analysis and changes in the pre- and post-drug treatment, creatinine clearance, and daily drug elimination rate constants. This allometric dose did not produce clinical toxicity in a control group of six dogs with intact kidneys given drug for 14 days. Dosage adjustments within the FI and FD groups were based on serum creatinine concentrations 10 days after surgery. Statistical analysis of morphological and functional parameters indicated that the FD method was significantly less toxic than the FI regimen.

A novel method for preparing liposome with a high capacity to encapsulate proteinous drugs: freeze-drying method.

A simple method for the preparation of liposome with high encapsulation efficiency was developed. A solution of L-asparaginase (A-ase) and a sonicated phospholipid were mixed together and the mixture was freeze-dried. The liposomes were regenerated by adding distilled water, followed by shaking with a Vortex mixer (FD method). Electron microscopic observation revealed that the liposomes prepared by this method have a multilamellar structure. The liposomes had approximately eight times as much encapsulating ability as those prepared by the ordinary thin film method.

The flow deviation method: An approach to store‐and‐forward communication network design

AbstractTwo problems relevant to the design of a store‐and‐forward communication network (the message routing problem and the channel capacity assignment problem) are formulated and are recognized to be essentially non‐linear, unconstrained multicommodity (m.c.) flow problems. A “Flow Deviation” (FD) method for the solution of these non‐linear, unconstrained m.c. flow problems is described which is quite similar to the gradient method for functions of continuous variables; here the concept of gradient is replaced by the concept of “shortest route” flow. As in the gradient method, the application of successive flow deviations leads to local minima. Finally, two interesting applications of the FD method to the design of the ARPA Computer Network are discussed.