• Journal of Applied and Pure Mathematics
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• v.5 no.5_6
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• pp.389-406
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• 2023

In the pursuit of enhancing image fusion techniques, this research presents a novel approach for fusing multimodal images, specifically infrared (IR) and visible (VIS) images, utilizing a combination of partial differential equations (PDE) and discrete cosine transformation (DCT). The proposed method seeks to leverage the thermal and structural information provided by IR imaging and the fine-grained details offered by VIS imaging create composite images that are superior in quality and informativeness. Through a meticulous fusion process, which involves PDE-guided fusion, DCT component selection, and weighted combination, the methodology aims to strike a balance that optimally preserves essential features and minimizes artifacts. Rigorous evaluations, both objective and subjective, are conducted to validate the effectiveness of the approach. This research contributes to the ongoing advancement of multimodal image fusion, addressing applications in fields like medical imaging, surveillance, and remote sensing, where the marriage of IR and VIS data is of paramount importance.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.763-779
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• 2011

In this paper we apply the Exp-function method to obtain traveling wave solutions of three nonlinear partial differential equations, namely, generalized sinh-Gordon equation, generalized form of the famous sinh-Gordon equation, and double combined sinh-cosh-Gordon equation. These equations play a very important role in mathematical physics and engineering sciences. The Exp-Function method changes the problem from solving nonlinear partial differential equations to solving a ordinary differential equation. Mainly we try to present an application of Exp-function method taking to consideration rectifying a commonly occurring errors during some of recent works.

• Journal of Korea Soil Environment Society
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• v.5 no.1
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• pp.3-12
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• 2000

The multi-region model, to describe preferential flow, is an equation representing solute transport in soils by dividing soil into numerous pore groups and using the hydraulic properties of the soil. As the model partial differential equation (PDE) is solved numerically with finite difference methods. a modified equivalent partial differential equation(MEPDE) of the partial differential equation of the multi-region model is derived to analyze the accuracy and consistency of the solution of the model PDE and the Von Neumann method is used to analyze the stability of the finite difference scheme. The evaluation obtained from the MEPDE indicated that the finite difference scheme was found to be consistent with the model PDE and had the second order accuracy The stability analysis is performed to analyze the model PDE with the amplification ratio and the phase lag using the Von Neumann method. The amplification ratio of the finite difference scheme gave non-dissipative results with various Peclet numbers and yielded the most high values as the Peclet number was one. The phase lag showed that the frequency component of the finite difference scheme lagged the true solution. From the result of the stability analysis for the model PDE, it is analyzed that the model domain should be discretized in the range of Pe < 1.0 and Cr < 2.0 to obtain the more accurate solution.

• Nuclear Engineering and Technology
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• v.55 no.6
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• pp.2305-2314
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• 2023

The governing equations of atmospheric dispersion most often taking the form of a second-order partial differential equation (PDE). Currently, typical computational codes for predicting atmospheric dispersion use the Gaussian plume model that is an analytic solution. A Gaussian model is simple and enables rapid simulations, but it can be difficult to apply to situations with complex model parameters. Recently, a method of solving PDEs using artificial neural networks called physics-informed neural network (PINN) has been proposed. The PINN assumes the latent (hidden) solution of a PDE as an arbitrary neural network model and approximates the solution by optimizing the model. Unlike a Gaussian model, the PINN is intuitive in that it does not require special assumptions and uses the original equation without modifications. In this paper, we describe an approach to atmospheric dispersion modeling using the PINN and show its applicability through simple case studies. The results are compared with analytic and fundamental numerical methods to assess the accuracy and other features. The proposed PINN approximates the solution with reasonable accuracy. Considering that its procedure is divided into training and prediction steps, the PINN also offers the advantage of rapid simulations once the training is over.

• East Asian mathematical journal
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• v.38 no.5
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• pp.603-610
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• 2022

In [6, 7] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous boundary conditions, compute the finite element solutions using standard FEM and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. They considered a partial differential equation with the input function f ∈ L²(Ω). In this paper we consider a PDE with the input function f ∈ H¹(Ω) and find the corresponding singular and dual singular functions. We also induce the corresponding extraction formula which are the basic element for the approach.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.3
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• pp.702-707
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• 2004

This article is concerned with container pose estimation using CCD a camera and a range sensor. In particular, the issues of characteristic point extraction and image noise reduction are described. The Euler-Lagrange equation for gaussian and random noise reduction is introduced. The alternating direction implicit(ADI) method for solving Euler-Lagrange equation based on partial differential equation(PDE) is applied. The vertex points as characteristic points of a container and a spreader are founded using k order curvature calculation algorithm since the golden and the bisection section algorithm can't solve the local minimum and maximum problems. The proposed algorithm in image preprocess is effective in image denoise. Furthermore, this proposed system using a camera and a range sensor is very low price since the previous system can be used without reconstruction.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.173-184
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• 2004

In this paper, we find the approximate solution of a second order nonlinear partial differential equation on a simple connected region in $R^2$. We transfer this problem to a new problem of second order nonlinear partial differential equation on a rectangle. Then, we transformed the later one to an equivalent optimization problem. Then we consider the optimization problem as a distributed parameter system with artificial controls. Finally, by using the theory of measure, we obtain the approximate solution of the original problem. In this paper also the global error in $L_1$ is controlled.

• Journal of Biomedical Engineering Research
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• v.41 no.3
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• pp.128-137
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• 2020

Cardiac electrophysiology studies often use simulation to predict how cardiac will behave under various conditions. To observe the cardiac tissue movement, it needs to use the high--resolution heart mesh with a sophisticated and large number of nodes. The higher resolution mesh is, the more computation time is needed. To improve computation speed and performance, parallel processing using multi-core processes and network computing resources is performed. In this study, we compared the computational speeds of CPU parallelization and GPU parallelization in virtual heart simulation for efficiently calculating a series of ordinary differential equations (ODE) and partial differential equations (PDE) and determined the optimal CPU and GPU parallelization architecture. We used 2D tissue model and 3D ventricular model to compared the computation performance. Then, we measured the time required to the calculation of ODEs and PDEs, respectively. In conclusion, for the most efficient computation, using GPU parallelization rather than CPU parallelization can improve performance by 4.3 times and 2.3 times in calculations of ODEs and PDE, respectively. In CPU parallelization, it is best to use the number of processors just before the communication cost between each processor is incurred.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1798-1803
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• 2003

In this work the dynamic heat transfer occurring in a cable penetration fire stop system built in the firewall of nuclear power plants is three-dimensionally investigated to develop a test-simulator that can be used to verify effectiveness of the sealants. The dynamic heat transfer can be described by a partial differential equation (PDE) and its initial and boundary conditions. For the shake of simplicity PDE is divided into two parts; one corresponding to the heat transfer in the axial direction and the other corresponding to the heat transfer on the vertical layers. Two numerical methods, SOR (Sequential Over-Relaxation) and FEM (Finite Element Method), are implemented to solve these equations respectively. The axial line is discretized, and SOR is applied. Similarly, all the layers are separated into finite elements, where the time and spatial functions are assumed to be of orthogonal collocation state at each element. The heat fluxes on the layers are calculated by FEM. It is shown that the penetration cable influences the temperature distribution of the fire stop system very significantly. The simulation results are shown in the three-dimensional graphics for the understanding of the transient temperature distribution in the fire stop system.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.10
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• pp.4108-4125
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• 2015

This paper presents a scalable coding method for depth images by considering the quality of synthesized images in virtual views. First, we design a new edge detection algorithm that is based on calculating the depth difference between two neighboring pixels within the depth map. By choosing different thresholds, this algorithm generates a scalable bit stream that puts larger depth differences in front, followed by smaller depth differences. A scalable scheme is also designed for coding depth pixels through a layered sampling structure. At the receiver side, the full-resolution depth image is reconstructed from the received bits by solving a partial-differential-equation (PDE). Experimental results show that the proposed method improves the rate-distortion performance of synthesized images at virtual views and achieves better visual quality.