• East Asian mathematical journal
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• v.33 no.1
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• pp.1-9
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• 2017

In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get accurate solution just by adding the singular part. This approach works for the case when we have the reasonably accurate stress intensity factor. In this paper we consider Poisson equations defined on a domain with a concave corner with Neumann boundary conditions. First we compute the stress intensity factor using the extraction formular, then find the regular part of the solution and the solution.

• Structural Engineering and Mechanics
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• v.61 no.5
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• pp.657-661
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• 2017

In this paper, it has been tried to propose a new semi analytical approach for solving nonlinear vibration of conservative systems. Hamiltonian approach is presented and applied to high nonlinear vibration systems. Hamiltonian approach leads us to high accurate solution using only one iteration. The method doesn't need any small perturbation and sufficiently accurate to both linear and nonlinear problems in engineering. The results are compared with numerical solution using Runge-Kutta-algorithm. The procedure of numerical solution are presented in detail. Hamiltonian approach could be simply apply to other powerfully non-natural oscillations and it could be found widely feasible in engineering and science.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.661-674
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• 2016

In [15] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution we could get accurate solution just by adding the singular part. This approach works for the case when we have the accurate stress intensity factor. In this paper we consider Poisson equations with mixed boundary conditions and show the method depends the accrucy of the stress intensity factor by considering two algorithms.

• Journal of Biomedical Engineering Research
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• v.30 no.1
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• pp.10-17
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• 2009

Accurate electroencephalography (EEG) forward calculation is of importance for the accurate estimation of neuronal electrical sources. Conventional studies concerning the EEG forward problems have investigated various factors influencing the forward solution accuracy, e.g. tissue conductivity values in head compartments, anisotropic conductivity distribution of a head model, tessellation patterns of boundary element models, the number of elements used for boundary/finite element method (BEM/FEM), and so on. In the present paper, we investigated the influence of modeling errors in the boundary element volume conductor models upon the accuracy of the EEG forward solutions. From our simulation results, we could confirm that accurate construction of boundary element models is one of the key factors in obtaining accurate EEG forward solutions from BEM. Among three boundaries (scalp, outer skull, and inner skull boundary), the solution errors originated from the modeling error in the scalp boundary were most significant. We found that the nonuniform error distribution on the scalp surface is closely related to the electrode configuration and the error distributions on the outer and inner skull boundaries have statistically meaningful similarity to the curvature distributions of the boundary surfaces. Our simulation results also demonstrated that the accumulation of small modeling errors could lead to considerable errors in the EEG source localization. It is expected that our finding can be a useful reference in generating boundary element head models.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.4
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• pp.301-327
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• 2019

The proper orthogonal decomposition (POD) method for time-dependent problems significantly reduces the computational time as it reduces the original problem to the lower dimensional space. Even a higher degree of reduction can be reached if the solution is smooth in space and time. However, if the solution is discontinuous and the discontinuity is parameterized e.g. with time, the POD approximations are not accurate in the reduced space due to the lack of ability to represent the discontinuous solution as a finite linear combination of smooth bases. In this paper, we propose to post-process the sample solutions and re-initialize the POD approximations to deal with discontinuous solutions and provide accurate approximations while the computational time is reduced. For the post-processing, we use the Gegenbauer reconstruction method. Then we regularize the Gegenbauer reconstruction for the construction of POD bases. With the constructed POD bases, we solve the given PDE in the reduced space. For the POD approximation, we re-initialize the POD solution so that the post-processed sample solution is used as the initial condition at each sampling time. As a proof-of-concept, we solve both one-dimensional linear and nonlinear hyperbolic problems. The numerical results show that the proposed method is efficient and accurate.

• Journal of Mechanical Science and Technology
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• v.15 no.6
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• pp.752-763
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• 2001

Although there are many different solution schemes proposed for multidimensional radiative transfer, reference solutions to benchmark these methods are very rare in the literature. In this paper we produced some accurate solutions for purely absorbing gray and nongray gases including H$_2$O and CO$_2$by using the discrete transfer method with sufficiently accurate T(sub)95 quadrature set. The spectral transmittances of the mixtures of H$_2$O and CO$_2$are estimated by using the narrow band model. The gray gas solutions are obtained for different absorption coefficients, and the nongray real gas solutions are obtained for different mixture fractions of H$_2$O and CO$_2$. The numerical solutions presented in this paper are proved to be sufficiently accurate as compared to the available exact solutions and they may be used as reference solutions in evaluating various solution schemes.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.9
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• pp.2329-2338
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• 1993

An accurate analysis procedure to solve the flow about a flat plate at various incidences has been developed. The Navier-Stokes equations of stream function and vorticity form are solved in a sufficiently large computational domain, in which the grid lines are mutually orthogonal. The details of the flow near the singularity at the tip of the plate is well captured by the analytic solution which is asymptotically matched to the numerically generated outer solution. The solution for each region is obtained iteratively : the solution of one (inner or outer) region uses that of the other as the boundary condition after each cycle. The resulting procedure is accurate everywhere and also computationally efficient as the singularity has been removed. It is applied to the flat plate for a wide range of Re : the results agree very well with the existing computation and experiment.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.785-794
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• 2018

In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous Dirichlet boundary condition with one corner singularity at the origin, and compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. This approach uses the polar coordinate and the cut-off function to control the singularity and the boundary condition. In this paper we consider Poisson equations with multiple singular points, which involves different cut-off functions which might overlaps together and shows the way of cording in FreeFEM++ to control the singular functions and cut-off functions with numerical experiments.

• Journal of Surface Science and Engineering
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• v.1 no.1
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• pp.5-13
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• 1967

Up to this date, numerous methods of analysis of electropling solutions are published. Some, however, need lots of works before reaching final results, or require high technique and special instruments, and also some are unaccurate due to unclearnes of end point. Like our undevelop countries, technicians of electroplating shops are most high school graduates or under, and have not much knowledge on chemistry. Furthermore, those technicians have to control their plating solutions by themselves without having enough analytical laboratory equipment . Therefore, in this paper the simplest, besides accurate method is investigated after comparing numerous methods published. Among the methods of copper determinations from acid and alkaline copper plating baths, EDTA titration method are chosen, due to these methods are the simpest and fastest for the evaluation of metal content, without requirng any special instrument. For acid copper solutions, chelate titrations were accurate enough. Since the end point of titration of chelate method is variable according to the kind of indicators and other metal's coexisitence as well as solution component, many difficulties were encountered from cyanide copper, on the contrary of acid copper bath. PAN , PV, and MX indicators were tried , but it is found that MX is the best. In chyanide solution ,due to cyanide is the masking reagent , elimination of this component is essential , and finally found that elimination CN-by precipitation with AgNO$_3$ solution was the simplest and the most accurate way among others. This method was very accurate for the new plating solutions even coexistence with organic brightners. However used solutions for long months running have to be predetermined the accurate copper value by thiosulfate method form time to time, before chelate titration by means of AgNO$_3$ precipitation. Always some constant deviations will be seen according to the solutions nature. Therefore those deviation values have to be compensated each time.

• Journal of Surface Science and Engineering
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• v.16 no.4
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• pp.199-214
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• 1983

Up to this date, numerous methods of analysis of electroplating solutions are published. Some, however, need lots of works before reaching final results, or require high technique and special instruments, and also some are unaccurate due to unclearnes of end point. Like our undevelope countries, technicians of electoplating shops are most high school gradutes or under, and have not much knowledge on chemistry. Furthermore, those technicians have to control their plating solutions by themselves without having enough analytical laboratory equiIJment. Therefore, in this paper the simplest, besides accurate method is investigated after comparing nu.merous methods published. Among the methods of 'copper determinations from acid and alkaline copper plating baths, EDT A titration method are chosen, due to these methods are the simplest and fastest for the evaluation of metal content, without requiring any special instrument. For acid copper solutions, chelate titrations were accurate enough. Since the end point of titration of chelate method is variable according to the kind of .indicators androther metal's coexsistence as well as solution comIJonent, many difficulties were encountered from cyanide' copper, on the contrary of acid copper bath. PAN, PV, and MX indicators were tried, but it is found that MX is the best. In cyanide solution, due to cyanide is the masking reagent, elimination of this component is essential, and finally found that elimination eN- by precipitation with AgN03 solution was the simplest and the most accurate way among others. This method was very accurate for the new plating solutions even coexistence with organic brightners. However used solutions for long months running have to be predetermined the accurate copper value by thiosulfate method from time to time, before chelate titration by means of AgN03 precipitation. Always some constant deviatioJ;ls will be seen according to the solutions nature. Therefore those deviation values have to be compensated each time.