The Experts below are selected from a list of 32808 Experts worldwide ranked by ideXlab platform
Tony Schonherr - One of the best experts on this subject based on the ideXlab platform.
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a flux splitting method for Hyperbolic Equation system of magnetized electron fluids in quasi neutral plasmas
2016Co-Authors: Rei Kawashima, Kimiya Komurasaki, Tony SchonherrAbstract:A flux-splitting method is proposed for the Hyperbolic-Equation system (HES) of magnetized electron fluids in quasi-neutral plasmas. The numerical fluxes are split into four categories, which are computed by using an upwind method which incorporates a flux-vector splitting (FVS) and advection upstream splitting method (AUSM). The method is applied to a test calculation condition of uniformly distributed and angled magnetic lines of force. All of the pseudo-time advancement terms converge monotonically and the conservation laws are strictly satisfied in the steady state. The calculation results are compared with those computed by using the elliptic-parabolic-Equation system (EPES) approach using a magnetic-field-aligned mesh (MFAM). Both qualitative and quantitative comparisons yield good agreements of results, indicating that the HES approach with the flux-splitting method attains a high computational accuracy.
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a Hyperbolic Equation system approach for magnetized electron fluids in quasi neutral plasmas
2015Co-Authors: Rei Kawashima, Kimiya Komurasaki, Tony SchonherrAbstract:A new approach using a Hyperbolic-Equation system (HES) is proposed to solve for the electron fluids in quasi-neutral plasmas. The HES approach avoids treatments of cross-diffusion terms which cause numerical instabilities in conventional approaches using an elliptic Equation (EE). A test calculation reveals that the HES approach can robustly solve problems of strong magnetic confinement by using an upwind method. The computation time of the HES approach is compared with that of the EE approach in terms of the size of the problem and the strength of magnetic confinement. The results indicate that the HES approach can be used to solve problems in a simple structured mesh without increasing computational time compared to the EE approach and that it features fast convergence in conditions of strong magnetic confinement.
R K Mohanty - One of the best experts on this subject based on the ideXlab platform.
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a new spline in tension method of o k 2 h 4 k 2 h 4 based on off step grid points for the solution of 1d quasi linear Hyperbolic partial differential Equations in vector form
2019Co-Authors: R K Mohanty, Gunjan KhuranaAbstract:In this paper, we propose a new three level implicit method based on half-step spline in tension method of order two in time and four in space for the solution of one-space dimensional quasi-linear Hyperbolic partial differential Equation of the form $$w_{tt}=K(x,t,w)w_{xx} + {\varphi }(x,t,w,w_{x},w_{t})$$ . We describe spline in tension approximations and its properties using two half-step grid points. The new method for one dimensional quasi-linear Hyperbolic Equation is obtained directly from the consistency condition. In this method we use three grid points for the unknown function w(x, t) and two half-step points for the known variable ‘x’ in x-direction. The proposed method when applied to Telegraphic Equation is shown to be unconditionally stable. Further, the stability condition for 1-D linear Hyperbolic Equation with variable coefficients is established. Our method is directly applicable to Hyperbolic Equations irrespective of the coordinate system which is the main advantage of our work. The proposed method for scalar Equation is extended to solve the system of quasi-linear Hyperbolic Equations. To assess the validity and accuracy, the proposed method is applied to solve several benchmark problems and numerical computations are provided to demonstrate the effectualness of the method.
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an unconditionally stable finite difference formula for a linear second order one space dimensional Hyperbolic Equation with variable coefficients
2005Co-Authors: R K MohantyAbstract:We propose a three level implicit unconditionally stable difference scheme of O(k^2+h^2) for the difference solution of second order linear Hyperbolic Equation u"t"[email protected](x,t)u"[email protected]^2(x,t)u=A(x,t)u"x"x+f(x,t), 00 subject to appropriate initial and Dirichlet boundary conditions, where A(x,t)>0, @a(x,t)>@b(x,t)>=0. The proposed formula is applicable to the problems having singularity at x=0. The resulting tri-diagonal linear system of Equations is solved by using Gauss-elimination method. Numerical examples are provided to illustrate the unconditionally stable character of the proposed method.
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an operator splitting technique for an unconditionally stable difference method for a linear three space dimensional Hyperbolic Equation with variable coefficients
2005Co-Authors: R K MohantyAbstract:We report a new three-step operator splitting method of O(k^2+h^2) for the difference solution of linear Hyperbolic Equation u"t"t+2@a(x,y,z,t)u"t+@b^2(x,y,z,t)u=A(x,y,z,t)u"x"x+B(x,y,z,t)u"y"y+C(x,y,z,t)u"z"z+f(x,y,z,t) subject to appropriate initial and Dirichlet boundary conditions, where @a(x,y,z,t)>@b(x,y,z,t)>0 and A(x,y,z,t)>0, B(x,y,z,t)>0, C(x,y,z,t)>0. The method is applicable to singular problems and stable for all choices of h>0 and k>0. The resulting system of algebraic Equations is solved by using a tri-diagonal solver. Computational results are provided to demonstrate the viability of the new method.
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an operator splitting method for an unconditionally stable difference scheme for a linear Hyperbolic Equation with variable coefficients in two space dimensions
2004Co-Authors: R K MohantyAbstract:A new three level implicit unconditionally stable operator splitting method of O(k^2+h^2) is proposed for the numerical solution of two space dimensional linear Hyperbolic Equation u"t"[email protected](x,y,t)u"[email protected]^2(x,y,t)u=A(x,y,t)u"x"x+B(x,y,t)u"y"y+f(x,y,t), 00 subject to appropriate initial and Dirichlet boundary conditions, where @a(x,y,t)>@b(x,y,t)>0, A(x,y,t)>0, B(x,y,t)>0. The resulting system of algebraic Equations is solved by two-step split method. The proposed method is applicable to the problems having singularity at x=0. Numerical results are provided to demonstrate the utility of the new method.
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an unconditionally stable difference scheme for the one space dimensional linear Hyperbolic Equation
2004Co-Authors: R K MohantyAbstract:Abstract An implicit three-level difference scheme of O(k2 + h2) is discussed for the numerical solution of the linear Hyperbolic Equation utt + 2αut + β2u = uxx + f(x, t), α > β ≥ 0, in the region Ω = {(x,t) ∥ 0 0} subject to appropriate initial and Dirichlet boundary conditions, where α and β are real numbers. We have used nine grid points with a single computational cell. The proposed scheme is unconditionally stable. The resulting system of algebraic Equations is solved by using a tridiagonal solver. Numerical results demonstrate the required accuracy of the proposed scheme.
Masahiro Yamamoto - One of the best experts on this subject based on the ideXlab platform.
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inverse source problem for the Hyperbolic Equation with a time dependent principal part
2017Co-Authors: Daijun Jiang, Yikan Liu, Masahiro YamamotoAbstract:Abstract In this paper, we investigate the inverse problem on determining the spatial component of the source term in the Hyperbolic Equation with a time-dependent principal part. Based on a Carleman estimate for general Hyperbolic operators, we prove a local stability result of Holder type in both cases of partial boundary and interior observation data. Numerically, we adopt the classical Tikhonov regularization to reformulate the inverse problem into a related optimization problem, for which we develop an iterative thresholding algorithm by using the corresponding adjoint system. Numerical examples up to three spatial dimensions are presented to demonstrate the accuracy and efficiency of the proposed algorithm.
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inverse problem for a Hyperbolic Equation with a finite set of boundary data
2017Co-Authors: Mourad Bellassoued, Masahiro YamamotoAbstract:In this chapter, we consider an inverse problem of determining multiple coefficients of the principal part of a scalar Hyperbolic Equation with Dirichlet boundary data.
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inverse source problem for a double Hyperbolic Equation describing the three dimensional time cone model
2015Co-Authors: Yikan Liu, Daijun Jiang, Masahiro YamamotoAbstract:In this paper, we consider the reconstruction of the nucleation rate in the three-dimensional time cone model, which turns out to be an inverse source problem for a double Hyperbolic Equation. More precisely, we attempt to recover a spatial component of the nucleation rate by partial interior observation data. After a direct derivation of a Hyperbolic-type governing Equation from the original model, we establish the well-posedness result for the forward problem by the classical Hyperbolic theory. To guarantee the validity of the reconstruction, we prove the two-sided global Lipschitz stability for the inverse problem based on a Carleman estimate. Motivated by the iterative thresholding algorithm for the same problem for Hyperbolic Equations, we develop an iterative thresholding algorithm for the identification. Extensive numerical experiments up to three spatial dimensions demonstrate the efficiency and accuracy of the algorithm, and detailed analysis of the computational performance is also provided.
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growth rate modeling and identification in the crystallization of polymers
2012Co-Authors: Yikan Liu, Masahiro YamamotoAbstract:Nucleation and growth mechanisms are important kinetics of the phase transformation model which arises in the crystallization of polymer materials. In each stage, the nucleation rate and growth rate are crucial coefficients describing the kinetics of the process as well as the properties of the specimens. Moreover, the identification of these physical parameters describing the nucleation or the growth mechanisms is essential for controlling the crystallization of polymers and so is a significant subject also from an industrial viewpoint. In this paper, we show that we can re-formulate the time cone approach of Cahn (1996 Mater. Res. Soc. Symp. Proc. 398 425–37) by a Hyperbolic governing Equation with the heterogeneous nucleation rate and spatially homogeneous growth rate. Then, on the basis of the Hyperbolic Equation, we investigate an inverse problem of determining the growth rate for an isothermal one-dimensional specimen. Our inverse problem is an inverse coefficient problem for a Hyperbolic Equation which is highly nonlinear with respect to the observation data. A two-step Tikhonov-type regularization method is proposed to reconstruct the growth rate provided with the final noisy observation data. Numerical prototype examples are presented to illustrate the validity and effectiveness of the proposed scheme.
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lipschitz stability in an inverse problem for a Hyperbolic Equation with a finite set of boundary data
2008Co-Authors: Mourad Bellassoued, D Jellali, Masahiro YamamotoAbstract:We consider an inverse problem of determining multiple coefficients of principal part of a scalar Hyperbolic Equation with Dirichlet boundary data. We prove the uniqueness and a Lipschitz stability estimate in the inverse problem with some observations on a suitable sub-boundary satisfying an appropriate geometrical condition. The key is a Carleman estimate for a Hyperbolic operator with variable coefficients.
Rei Kawashima - One of the best experts on this subject based on the ideXlab platform.
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a flux splitting method for Hyperbolic Equation system of magnetized electron fluids in quasi neutral plasmas
2016Co-Authors: Rei Kawashima, Kimiya Komurasaki, Tony SchonherrAbstract:A flux-splitting method is proposed for the Hyperbolic-Equation system (HES) of magnetized electron fluids in quasi-neutral plasmas. The numerical fluxes are split into four categories, which are computed by using an upwind method which incorporates a flux-vector splitting (FVS) and advection upstream splitting method (AUSM). The method is applied to a test calculation condition of uniformly distributed and angled magnetic lines of force. All of the pseudo-time advancement terms converge monotonically and the conservation laws are strictly satisfied in the steady state. The calculation results are compared with those computed by using the elliptic-parabolic-Equation system (EPES) approach using a magnetic-field-aligned mesh (MFAM). Both qualitative and quantitative comparisons yield good agreements of results, indicating that the HES approach with the flux-splitting method attains a high computational accuracy.
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a Hyperbolic Equation system approach for magnetized electron fluids in quasi neutral plasmas
2015Co-Authors: Rei Kawashima, Kimiya Komurasaki, Tony SchonherrAbstract:A new approach using a Hyperbolic-Equation system (HES) is proposed to solve for the electron fluids in quasi-neutral plasmas. The HES approach avoids treatments of cross-diffusion terms which cause numerical instabilities in conventional approaches using an elliptic Equation (EE). A test calculation reveals that the HES approach can robustly solve problems of strong magnetic confinement by using an upwind method. The computation time of the HES approach is compared with that of the EE approach in terms of the size of the problem and the strength of magnetic confinement. The results indicate that the HES approach can be used to solve problems in a simple structured mesh without increasing computational time compared to the EE approach and that it features fast convergence in conditions of strong magnetic confinement.
Ozgur Yildirim - One of the best experts on this subject based on the ideXlab platform.
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on stability of a third order of accuracy difference scheme for Hyperbolic nonlocal bvp with self adjoint operator
2013Co-Authors: Allaberen Ashyralyev, Ozgur YildirimAbstract:A third order of accuracy absolutely stable difference schemes is presented for nonlocal boundary value Hyperbolic problem of the differential Equations in a Hilbert space with self-adjoint positive definite operator . Stability estimates for solution of the difference scheme are established. In practice, one-dimensional Hyperbolic Equation with nonlocal boundary conditions is considered.
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stable difference schemes for the Hyperbolic problems subject to nonlocal boundary conditions with self adjoint operator
2011Co-Authors: Allaberen Ashyralyev, Ozgur YildirimAbstract:Abstract In the present paper the first and second orders of accuracy difference schemes for the numerical solution of multidimensional Hyperbolic Equations with nonlocal boundary and Dirichlet conditions are presented. The stability estimates for the solution of difference schemes are obtained. A method is used for solving these difference schemes in the case of one dimensional Hyperbolic Equation.
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second order of accuracy stable difference schemes for Hyperbolic problems subject to nonlocal conditions with self adjoint operator
2011Co-Authors: Allaberen Ashyralyev, Ozgur YildirimAbstract:In the present paper, two new second order of accuracy absolutely stable difference schemes are presented for the nonlocal boundary value problem {d2u(t)dt2+Au(t) = f(t) (0≤t≤1),u(0) = ∑ j = 1nαju(λj)+φ,ut(0) = ∑ j = 1nβjut(λj)+ψ,0<λ1<λ2<…<λn≤1 for differential Equations in a Hilbert space H with the self‐adjoint positive definite operator A. The stability estimates for the solutions of these difference schemes are established. In practice, one‐dimensional Hyperbolic Equation with nonlocal boundary conditions and multidimensional Hyperbolic Equation with Dirichlet conditions are considered. The stability estimates for the solutions of difference schemes for the nonlocal boundary value Hyperbolic problems are obtained and the numerical results are presented to support our theoretical statements.