Finite integration technique

A particularly powerful tool is the well established Elastodynamic Finite Integration Technique (EFIT), basically formulated by Fellinger et al. 

The Mie theory [1] and the T-matrix method [4] are very efficient for (multilayered) spheres and axisymmetric particles (with moderate aspect ratios), respectively. Several methods, applicable to particles of arbitrary shapes, have been used in plasmonic simulations the boundary element method (BEM) [5, 6], the DDA [7-9], the finite-difference time-domain method (FDTD) [10, 11], the finite element method (FEM] [12,13], the finite integration technique (FIT) [14] and the null-field method with discrete sources (NFM-DS) [15,16]. There is also quasi-static approximation for spheroids [12], but it is not discussed here. 

In this paper, the FIT (Finite Integration Technique) for the quasi static condition has been applied to evaluate the electromagnetic (EM) field interaction with the cells in different frequency radiation. The influences of the cells... 

The CST EMS simulator is an interactive package that uses Finite Integration Technique analysis (FIT) to solve two dimensional electrostatic problems. 

The finite integration technique suffers somewhat from a deficiency in being able to model very complicated cavities including curved boundaries with high precision, but the usage of the perfect boundary approximation eliminate this deficiency [123],... 

Fig. 3.18. Normalized differential scattering cross-sections of an oblate cylinder with ksb = 15 and 2ksa = 7.5. The cmves are computed with the TAXSYM routine, discrete somces method (DSM), multiple multipole method (MMP), discrete dipole approximation (DDA) and finite integration technique (CST)...

Fig. 3.21. Normalized differential scattering cross-sections of a dielectric hexagonal prism computed with the TNONAXSYM routine and the finite integration technique (CST)...

A. Clebsch, Uber die Reflexion an einer Kugelflache. J. Math. 61, 195 (1863) M. Clemens, T. Weiland, Discrete electromagnetism with the finite integration technique. PIER 32, 65 (2001)... 

Finite difference techniques are used to generate molecular dynamics trajectories with continuous potential models, which we will assume to be pairwise additive. The essential idea is that the integration is broken down into many small stages, each separated in time by a fixed time 6t. The total force on each particle in the configuration at a time t is calculated as the vector sum of its interactions with other particles. From the force we can determine the accelerations of the particles, which are then combined with the positions and velocities at a time t to calculate the positions and velocities at a time t + 6t. The force is assumed to be constant during the time step. The forces on the particles in their new positions are then determined, leading to new positions and velocities at time t - - 2St, and so on. 

Export processes are often more complicated than the expression given in Equation 7, for many chemicals can escape across the air/water interface (volatilize) or, in rapidly depositing environments, be buried for indeterminate periods in deep sediment beds. Still, the majority of environmental models are simply variations on the mass-balance theme expressed by Equation 7. Some codes solve Equation 7 directly for relatively large control volumes, that is, they operate on "compartment" or "box" models of the environment. Models of aquatic systems can also be phrased in terms of continuous space, as opposed to the "compartment" approach of discrete spatial zones. In this case, the partial differential equations (which arise, for example, by taking the limit of Equation 7 as the control volume goes to zero) can be solved by finite difference or finite element numerical integration techniques. 

Any nonnegative function which has a finite integral over the range of drop sizes may serve as a size-distribution function. However, to form a valid basis for statistical inferences, the distribution of each parameter involved in the chosen distribution must be known. Because the distributions of the parameters often present overwhelming mathematical difficulties, considerable care must be exercised in using various curvefitting techniques which introduce new parameters into the distribution. 

A finite element method is employed to study the nonlinear dynamic effect of a strong wind gust on a cooling tower. Geometric nonlinearities associated with finite deformations of the structure are considered but the material is assumed to remain elastic. Load is applied in small increments and the equation of motion is solved by a step-by-step integration technique. It has been found that the cooling tower will collapse under a wind gust of maximum pressure 1.2 psi. 13 refs, cited. 

A common method for solving partial differential equations (PDEs) is known as the method of lines. Here, finite difference approximations for spatial derivatives are used to convert a PDE model to a large set of ordinary differential equations, which are then solved using any of the ODE integration techniques discussed earlier. 

Bellman (1957) has suggested that the equation may be integrated by a finite difference technique ( Dynamic Programming, p. 254), but he acknowledges the likelihood of computational difficulties and is led to formulate a discrete version of the problem. Fortunately, in the case we shall be concerned with the method of characteristics is well suited to the integration of these equations. 

Finite difference techniques are used to generate molecular dynamics trajectories with continuous potential models, which we will assume to be pairwise additive. The essential idea is that the integration is broken down into many small stages, each separated in time by a fixed time fit. The total force on each particle in the configuration at a time t is... 

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