• Structural Engineering and Mechanics
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• v.27 no.6
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• pp.683-696
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• 2007

This article is concerned with the presentation of a time-domain BEM approach applied to the solution of the scalar wave equation for 2D problems. The basic idea is quite simple: the basic variables of the problem at time $t_n$ (potential and flux) are computed with the results related to the potential and to its time derivative at time $t_{n-1}$ playing the role of "initial conditions". This time-marching scheme needs the computation of the potential and its time derivative at all boundary nodes and internal points, as well as the entire discretization of the domain. The convolution integrals of the standard time-domain BEM formulation, however, are not computed; the matrices assembled, only at the initial time interval, are those related to the potential, flux and to the potential time derivative. Two examples are presented and discussed at the end of the article, in order to verify the accuracy and potentialities of the proposed formulation.

• Structural Engineering and Mechanics
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• v.23 no.3
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• pp.263-278
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• 2006

This work presents a time-truncation scheme, based on the Lagrange interpolation polynomial, for the solution of the two-dimensional scalar wave problem by the time-domain boundary element method. The aim is to reduce the number of stored matrices, due to the convolution integral performed from the initial time to the current time, and to keep a compromise between computational economy and efficiency and the numerical accuracy. In order to verify the accuracy of the proposed formulation, three examples are presented and discussed at the end of the article.

• Current Optics and Photonics
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• v.5 no.5
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• pp.491-499
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• 2021

A scalar Fourier modal method for the numerical analysis of the scalar wave equation in inhomogeneous space with an arbitrary permittivity profile, is proposed as a novel theoretical embodiment of Fourier optics. The modeling of devices and systems using conventional Fourier optics is based on the thin-element approximation, but this approach becomes less accurate with high numerical aperture or thick optical elements. The proposed scalar Fourier modal method describes the wave optical characteristics of optical structures in terms of the generalized transmittance function, which can readily overcome a current limitation of Fourier optics.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.509-518
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• 2001

The purpose of this paper is to propose a numerical algorithm for the problem of coefficient identification of the scalar wave equation based on a local observation on the boundary: Determine the unknown coefficient function with the knowledge of simultaneous Dirichlet and Neumann boundary values on a part of boundary. To find the unknown coefficient function, the unknown Neumann boundary value is also identified. We recast our inverse problem to variational problem. The gradient method is applied to find the minimizing functions. We confirm the effectiveness of our algorithm by numerical experiments.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.8
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• pp.140-152
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• 1995

Derived was the scalar wave equation of optical fibers. Based on the derived equation, the dispersion characteristics of arbitrarily profiled fibers were analyzed. We applied the 1-D FEM employing quadratic interpolation fucntions to solve the scalar wave equation. To find the optimum index distribution of a fiber that has the ultra-low total dispersion, we analyzed QC fibers as objects. Adding 2$_{nd}$ and 3$_{rd}$ clads to DC fiber, we investigated the change of dispersion characteristics. We found the QC fiber parameters for which the dispersion was ultra-low flattened, less than 0.5 ps/km.nm for ${\lambda}=1.4~1.6{\mu}m$, and the dispersion value was as low as 0.20 ps/km.nm at ${\lambda}=1.55{\mu}m$.

• Structural Engineering and Mechanics
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• v.51 no.4
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• pp.685-705
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• 2014

This paper presents a new formulation for forward scalar wave simulations in semi-infinite media. Perfectly-Matched-Layers (PMLs) are used as a wave absorbing boundary layer to surround a finite computational domain truncated from the semi-infinite domain. In this work, a hybrid formulation was developed for the simulation of scalar wave motion in two-dimensional PML-truncated domains. In this formulation, displacements and stresses are considered as unknowns in the PML domain, while only displacements are considered to be unknowns in the interior domain. This formulation reduces computational cost compared to fully-mixed formulations. To obtain governing wave equations in the PML region, complex coordinate stretching transformation was introduced to equilibrium, constitutive, and compatibility equations in the frequency domain. Then, equations were converted back to the time-domain using the inverse Fourier transform. The resulting equations are mixed (contain both displacements and stresses), and are coupled with the displacement-only equation in the regular domain. The Newmark method was used for the time integration of the semi-discrete equations.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1131-1145
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• 2021

In this article, we study the Klein-Gordon-Maxwell equations arising from a semilocal gauge field model. This model describes the interaction of two complex scalar fields and one gauge field, and generalizes the classical Klein-Gordon equation coupled with the Maxwell electrodynamics. We prove that there exist infinitely many standing wave solutions for p ∈ (2, 6) which are radially symmetric. Here, p comes from the exponent of the potential of scalar fields. We also prove the nonexistence of nontrivial solutions for the critical case p = 6.

• Korean Journal of Optics and Photonics
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• v.6 no.2
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• pp.156-164
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• 1995

Based on the scalar wave equation of optical fibers, the dispersion characteristics of arbitrarily profiled fibers were analyzed. We used the I-D FEM employing quadratic interpolation fucntions to solve the scalar wave equation. We simulated the DC optical fibers as objects, and searched for the refractive index distribution to minimize the total dispersion. In DC fibers, we found the design parameters for which the total dispersion was almost zero at $\lambda=1.3{\mu}m and 1.55{\mu}m$ simultaneously. We also found the design parameters where the dispersion was flattened, less than 1.0 ps/km.nm for$\lambda=1.4~1.7{\mu}m$1. and the dispersion was as low as 0.65 ps/km.nm at $\lambda=1.55{\mu}m$..

• Economic and Environmental Geology
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• v.29 no.2
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• pp.183-192
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• 1996

Much computing time and large computer memory are needed to solve the wave equation in a large complex subsurface layer using finite difference method. The time and memory can be reduced by decreasing the number of grid per minimun wave length. However, decrease of grid may cause numerical dispersion and poor accuracy. In this study, we present 49 points weighted average method which save the computing time and memory and improve the accuracy. This method applies a new weighted average to the coordinate determined by transforming the coordinate of conventional 5 points finite difference stars to $0^{\circ}$ and $45^{\circ}$, 25 points finite differenc stars to $0^{\circ}$, $26.56^{\circ}$, $45^{\circ}$, $63.44^{\circ}$ and 49 finite difference stars to $0^{\circ}$, $18.43^{\circ}$, $33.69^{\circ}$, $45^{\circ}$, $56.30^{\circ}$, $71.56^{\circ}$. By this method, the grid points per minimum wave length can be reduced to 2.5, the computing time to $(2.5/13)^3$, and the required core memory to $(2.5/13)^4$ computing with the conventional method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.2
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• pp.113-120
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• 2021

The wave-propagation phenomenon in an infinite medium has been used to describe the physics in many fields of engineering and natural science. Analytical or numerical methods have been developed to obtain solutions to problems related to the wave-propagation phenomenon. Energy radiation into infinite regions must be accurately considered for accurate solutions to these problems; hence, various numerical and mechanical models as well as boundary conditions have been developed. This paper proposes a new boundary condition that can be applied to scalar-wave or horizontally-polarized shear-wave (or SH-wave) propagation problems in layered waveguides. A governing equation is obtained for the SH waves by applying finite-element discretization in the vertical direction of the waveguide and subsequently modified to derive the boundary condition for the infinite region of the waveguide. Using the orthogonality of the eigenmodes for the SH waves in a layered waveguide, the new boundary condition is shown to be equivalent to the existing root-finding absorbing boundary condition; further, the accuracy is shown to increase with the degree of the new boundary condition, and its stability can be proven. The accuracy and stability are then demonstrated by applying the proposed boundary condition to wave-propagation problems in layered waveguides.