In this paper, the precorrected-FFT method is used to solve the electromagnetic scattering from two-dimensional cavities of arbitrary shape. The integral equation is discretized by the method of moments and the resultant matrix equation is solved iteratively by the generalized conjugate residual method. Instead of directly computing the matrix-vector multiplication, which requires N² operations, this approach reduces the computation complexity to O(N log N) as well as avoids the storage of large matrices. At the same time, a technique known as the complexifying k is applied to accelerate the convergence of the iterative method in solving this resonance problem. Some examples are considered and excellent agreements of radar cross sections between these computed using the present method and those from the direct solution are observed, demonstrating the feasibility and efficiency of the present method. / Singapore-MIT Alliance (SMA)

This paper presents an accurate and efficient method-of-moments solution of the electrical-field integral equation (EFIE) for large, three-dimensional, arbitrarily shaped objects. In this method, the generalized conjugate residual method (GCR) is used to solve the matrix equation iteratively and the precorrected-FFT technique is then employed to accelerate the matrix-vector multiplication in iterations. The precorrected-FFT method eliminates the need to generate and store the usual square impedance matrix, thus leading to a great reduction in memory requirement and execution time. It is at best an O(N log N) algorithm and can be modified to fit a wide variety of systems with different Green’s functions without excessive effort. Numerical results are presented to demonstrate the accuracy and computational efficiency of the technique. / Singapore-MIT Alliance (SMA)

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Boundary-contact problems (BCPs) are studied within the frames of classical mathematical theory of elasticity and plasticity elaborated by Landau, Kupradze, Timoshenko, Goodier, Fichera and many others on the basis of analysis of two- and three-dimensional boundary value problems for linear partial differential equations. A great attention is traditionally paid both to theoretical investigations using variational methods and boundary singular integral equations (Muskhelishvili) and construction of solutions in the form that admit efficient numerical evaluation (Kupradze). A special family of BCPs considered by Shtaerman, Vorovich, Alblas, Nowell, and others arises within the frames of the models of squeezing thin multilayer elastic sheets. We show that mathematical models based on the analysis of BCPs can be also applied to modeling of the clich\'-surface printing contacts and paper surface compressibility in flexographic printing. The main result of this work is formulation and complete investigation of BCPs in layered structures, which includes both the theoretical (statement of the problems, solvability and uniqueness) and applied parts (approximate and numerical solutions, codes, simulation). We elaborate a mathematical model of squeezing a thin elastic sheet placed on a stiff base without friction by weak loads through several openings on one of its boundary surfaces. We formulate and consider the corresponding BCPs in two- and three-dimensional bands, prove the existence and uniqueness of solutions, and investigate their smoothness including the behavior at infinity and in the vicinity of critical points. The BCP in a two-dimensional band is reduced to a Fredholm integral equation (IE) with a logarithmic singularity of the kernel. The theory of logarithmic IEs developed in the study includes the analysis of solvability and development of solution techniques when the set of integration consists of several intervals. The IE associated with the BCP is solved by three methods based on the use of Fourier-Chebyshev series, matrix-algebraic determination of the entries in the resulting infinite system matrix, and semi-inversion. An asymptotic theory for the BCP is developed and the solutions are obtained as asymptotic series in powers of the characteristic small parameter. We propose and justify a technique for the solution of BCPs and boundary value problems with boundary conditions of mixed type called the approximate decomposition method (ADM). The main idea of ADM is simplifying general BCPs and reducing them to a chain of auxiliary problems for 'shifted' Laplacian in long rectangles or parallelepipeds and then to a sequence of iterative problems such that each of them can be solved (explicitly) by the Fourier method. The solution to the initial BCP is then obtained as a limit using a contraction operator, which constitutes in particular an independent proof of the BCP unique solvability. We elaborate a numerical method and algorithms based on the approximate decomposition and the computer codes and perform comprehensive numerical analysis of the BCPs including the simulation for problems of practical interest. A variety of computational results are presented and discussed which form the basis for further applications for the modeling and simulation of printing-plate contact systems and other structures of flexographic printing. A comparison with finite-element solution is performed.

This study is to develop a 2D fully nonlinear numerical wave tank used to investigate the wave-induced dynamic properties of a dual pontoon floating structure (DPFS) with a liquid container on the top. The nonlinear numerical wave tank, developed based on the velocity potential function and the boundary element method (BEM), is to simulate dynamic properties including sway, heave, roll, and tension response. In addition, a physical model of the dual floating pontoon is tested in a hydrodynamic wave tank to validate the numerical model for simulation of wave and structure interaction. In the numerical model, a boundary integral equation method (BIEM) with linear element scheme is applied to establish a 2D fully nonlinear numerical wave tank (NWT). The nonlinear free surface condition is treated by combining the Mixed Eulerian and Lagrangian method (MEL), the fourth-order Runge-Kutta method (RK4) and a cubic spline scheme. The second-order Stokes wave theory is used to generate the velocity flux on the input boundary. Numerical damping zones are deployed at both ends of the NWT to dissipate or absorb the transmitted and reflected waves. Acceleration potential method and modal decomposition method are adopted to solve the unsteady potential functions £X1,t and £X2,t, while the system of motion equation is established according to Newton's 2nd law. Finally, the RK4 is applied to predict the motion of the platform, and the variation of free surface. As for the hydrodynamic laboratory model test, an image process scheme is applied to trace the floating structure motion and the variation of water surface inside the sloshing tank, while the mooring tension is measured by a load cell and stored in a data logger. The comparisons of numerical simulations and experimental data indicate that the numerical predictions are larger than measurements especially near the resonance frequency. This discrepancy is probably due to the fluid viscous effect. To overcome this problem and maintain the calculation efficiency, an uncoupled damping coefficient obtained through a damping ratio (£a=C/Ccr=0.02) is incorporated into the vibration system. Results reveal that responses of body motion near the resonant frequencies of each mode have significantly reduced and close to the measurements. Therefore, the suitable value of the damping ratio for the floating platform is £a=0.02. Then the numerical model with a damping ratio is applied to investigate the dynamic properties of the floating platform for different arrangements, including different mooring angle, spring constant, spacing, and the liquid container. Results demonstrate that the resonant frequency of each mode, responses of body motion and mooring tensions change along with the settings. As a whole, the platform with smaller mooring angle, longer spacing between the pontoons, higher water depth and wider width of the liquid container has relatively stable body motions and less mooring tension. Finally, the comparisons of the effects of random and regular waves on the floating structure illustrate that the variation of water surface in the liquid container is much severe in random waves than in regular waves such that the interaction between liquid and floating structure is more chaotic and thus reduces the amplitude of each response mode. As a result, the mooring tensions for random waves become much gentler than the regular waves. Key words: Boundary integral equation method; fully nonlinear numerical wave tank; dual pontoon floating structure

A new full-wave surface impedance integral equation method is presented for three-dimensional arbitrary-shaped interconnect parasitic extraction in layered media. Various new ways of applying voltage and current excitations for electromagnetic-circuit simulation are introduced. A new algorithm is proposed for matrix formation of electromagnetic-circuit simulation, low frequency solution and layered media so that it can be easily integrated to a Rao-Wilton-Glisson based method of moment code. Two mixed potential integral equation forms of the electric field integral equation are adapted along with the Michalski-Mosig formulations for layered kernels to model electromagnetic interactions of interconnects in layered media over a conducting substrate. The layered kernels are computed directly for controllable accuracy. The proposed methods are validated against existing methods for both electromagnetic and electromagnetic-circuit problems.

In this thesis, we have compared between dual-core fiber coupler with photonic crystal fiber coupler. From Surface Integral Equation Method derived from Maxwell¡¦s equations, we can simulate tapered fiber coupler, dual-core fiber coupler and photonic crystal fiber coupler. By analyzing the propagating characteristics and performance of these couplers, we hope to discuss between their advantages and dis-advantages. We have found that at the same parameters, conventional fiber coupler¡¦s coupling length is roughly half compared to photonic crystal coupler. In terms of bandwidth, photonic crystal coupler aided by air-hole tuning can achieve multiples times larger than conventional fiber coupler. So, we believe that in communication networks with a lust of bandwidth, photonic crystal coupler can definitely live up its expectations.

A single-mode fused biconical 2¡Ñ2 coupler for polarization beamsplitting is fabricated in this thesis. We use simple fused and tapered method to fabricate the polarization beamsplitter(PBS) stably, and then we can get polarization maintaining in the output fibers. Without changing the manufacturing process, we design the device with special combination of fabrication parameters. We have achieved an extinction ratio of 25.78dB at the throughput port and 27.16dB at the coupled port. A usable spectral window as broad as 37nm and 27nm with an extinction ratio larger than 15dB for both ports is obtained. The excess loss is about 0.3dB. Based on a full-wave numerical approach, the performance of the PBS can be well modeled. We get good agreement between the measured and simulated results.

This paper is to investigate the wave-induced dynamic properties of the floating platform for cage aquaculture. Considering the calculation efficiency and its applicability, this problem is simplified by: (1) assuming the flow field is inviscid, incompressible and irrotational; (2) the form drag and inertia drag on the fish net is calculated by the modified Morison equation (or Morison type equation of relative motion), including the material and geometric properties; (3) the moorings is treated as a symmetric linear spring system and the influence of hydrodynamic forces on the mooring lines is neglected; and (4) the net-volume is assumed as un-deformable to avoid the inversely prolonging computing time because the mass of fish net with is too light comparing with the mass of floating platform and cause the marching time step tremendously small to reach the steady-state condition which may lead to larger numerical errors (e.g. truncation errors) in computation. The BIEM with linear element scheme is applied to establish a 2D fully nonlinear numerical wave tank (NWT). The nonlinear free surface condition is treated by combining the Mixed Eulerian and Lagrangian method (MEL), the fourth-order Runge-Kutta method (RK4) and the cubic spline scheme. The second-order Stokes wave theory is adopted to give the velocity on the input boundary. Numerical damping zones are deployed at both ends of the NWT to dissipate or absorb the transmitted and reflected wave energy. The velocity and acceleration fields should be solved simultaneously in order to obtain the wave-induced dynamic property of the floating platform. Thus, both the acceleration potential method and modal decomposition method are adopted to solve the wave forces on the floating body, while the wave forces on the fish net are calculated by the modified Morison equation. According to Newton¡¦s second law, the total forces on the gravity center of the floating platform form the equation of motion. Finally, the RK4 is applied to predict the displacement and velocity of the platform. Firstly, the NWT is validated by comparing the wave elevation, internal velocity and acceleration with those from the second-order Stokes wave theory. Moreover, the numerical damping zone is suitable for long time simulation with a wide range of wave depth. The simulated results on wave-body interactions of fixed or freely floating body also indicate good agreement with those of other published results. Secondly, in the case of the interaction of waves and the floating platform, the simulated results show well agreement with experimental data, except at the vicinity of resonant frequency of roll and heave motions. This discrepancy is due to the fluid viscous effect. To overcome this problem and maintain the calculation efficiency, an uncoupled damping coefficient obtained by a damping ratio (£i=0.1 ) is incorporated into the vibration system. Results reveal that responses of body motion near the resonant frequencies of each mode have significant reduction and close to the experimental data. Moreover, the results are also consistent well with experiments in different wave height, mooring angle, water depth either with or without fish net. Therefore, the suitable value of the damping ratio for the floating platform is £i=0.1. Finally, the present model is applied to investigate the dynamic properties of the floating platform under different draft, width, spacing, spring constant, mooring angle and depth of fish net. Results reveal that the resonant frequency and response of body motion, mooring force, reflection and transmission coefficients and wave energy will be changed. According to the resonant response, the platform with shallower draft, larger width, longer spacing between two pontoons, smaller spring constants, or deeper depth of fish net has more stable body motions and smaller mooring forces. Irregular wave cases are presented to illustrate the relationship with the regular wave cases. Results indicate that the dynamic responses of body motion and the reflection coefficient in irregular waves have similar trend with regular waves. However, in the irregular wave cases, the resonant frequency is moved to the higher frequency. Similarly, resonant response function is smaller but wider, which is due to the energy distribution in the wave spectrum.

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