Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics

Boe-Shong Hong

doi:doi:10.11648/j.acm.20140305.12

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Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics

Boe-Shong Hong

Published in Applied and Computational Mathematics (Volume 3, Issue 5)

Received: 13 August 2014 Accepted: 11 September 2014 Published: 20 September 2014

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Abstract

Scientists and engineers encounter many kinds of parabolic or hyperbolic distributed dynamics, which are often with inhomogeneous boundary conditions in practice. Boundary inhomogeneity makes the dynamics essentially nonlinear, which prevents the Hilbert space from being applied for modal decomposition and intelligent computation. Thus, this paper systematically deals with this situation via the conversion of the boundary inhomogeneity to a virtual source in conjunction with boundary homogeneity. For such a purpose, the 2D transfer-function is developed based on the Laplace-Galerkin integral transform as the main tool of this conversion. A section of numerical visualization is included to explore the topology of the virtual-source solution. Some interesting findings therein will be addressed.

Published in	Applied and Computational Mathematics (Volume 3, Issue 5)
DOI	10.11648/j.acm.20140305.12
Page(s)	197-204
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Inhomogeneous Boundary Conditions, nD Transfer Function Models, Robin Boundary Conditions, Sturm-Liouville Systems

References

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[2]	B.-S. Hong and C.-Y. Chou, “Realization of thermal inertia in frequency domain,” Entropy, vol. 16, pp. 1101-1121, 2014.
[3]	B.-S. Hong and C.-Y. Chou, “Energy transfer modelling of active thermoacoustic engines via Lagrangian thermoacoustic dynamics,” Energy Convers. Manage., vol. 84, pp. 73-79, 2014.
[4]	B.-S. Hong, V. Yang, and A. Ray, “Robust feedback control of combustion instability with modeling uncertainty,” Combust. Flame, vol. 120, pp. 91-106, 2000.
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[10]	E. Okada, M. Schweiger, S. R. Arridge, M. Firbank, and D. T. Delpy, “Experimental validation of Monte Carlo and finite-element methods for the estimation of the optical path length in inhomogeneous tissue,” Applied Optics, vol. 35, no. 19, pp. 3362-3371, 1996.
[11]	F. Bay, V. Labbe, Y. Favennec, and J. L. Chenot, “A numerical model for induction heating processes coupling electromagnetism and thermomechanics,” Int. J. Numer. Meth. Engng, vol. 58, pp. 839–867, 2003.
[12]	B. Jin, “Conjugate gradient method for the Robin inverse problem, associated with the Laplace equation,” Int. J. Numer. Meth. Engng, vol. 71, pp. 433–453, 2007.
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Boe-Shong Hong. (2014). Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics. Applied and Computational Mathematics, 3(5), 197-204. https://doi.org/10.11648/j.acm.20140305.12

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ACS Style

Boe-Shong Hong. Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics. Appl. Comput. Math. 2014, 3(5), 197-204. doi: 10.11648/j.acm.20140305.12

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AMA Style

Boe-Shong Hong. Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics. Appl Comput Math. 2014;3(5):197-204. doi: 10.11648/j.acm.20140305.12

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@article{10.11648/j.acm.20140305.12,
  author = {Boe-Shong Hong},
  title = {Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {5},
  pages = {197-204},
  doi = {10.11648/j.acm.20140305.12},
  url = {https://doi.org/10.11648/j.acm.20140305.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140305.12},
  abstract = {Scientists and engineers encounter many kinds of parabolic or hyperbolic distributed dynamics, which are often with inhomogeneous boundary conditions in practice. Boundary inhomogeneity makes the dynamics essentially nonlinear, which prevents the Hilbert space from being applied for modal decomposition and intelligent computation. Thus, this paper systematically deals with this situation via the conversion of the boundary inhomogeneity to a virtual source in conjunction with boundary homogeneity. For such a purpose, the 2D transfer-function is developed based on the Laplace-Galerkin integral transform as the main tool of this conversion. A section of numerical visualization is included to explore the topology of the virtual-source solution. Some interesting findings therein will be addressed.},
 year = {2014}
}

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TY  - JOUR
T1  - Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics
AU  - Boe-Shong Hong
Y1  - 2014/09/20
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140305.12
DO  - 10.11648/j.acm.20140305.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 197
EP  - 204
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140305.12
AB  - Scientists and engineers encounter many kinds of parabolic or hyperbolic distributed dynamics, which are often with inhomogeneous boundary conditions in practice. Boundary inhomogeneity makes the dynamics essentially nonlinear, which prevents the Hilbert space from being applied for modal decomposition and intelligent computation. Thus, this paper systematically deals with this situation via the conversion of the boundary inhomogeneity to a virtual source in conjunction with boundary homogeneity. For such a purpose, the 2D transfer-function is developed based on the Laplace-Galerkin integral transform as the main tool of this conversion. A section of numerical visualization is included to explore the topology of the virtual-source solution. Some interesting findings therein will be addressed.
VL  - 3
IS  - 5
ER  -

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Author Information

Boe-Shong Hong

Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi 62012, Taiwan

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Boe-Shong Hong. (2014). Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics. Applied and Computational Mathematics, 3(5), 197-204. https://doi.org/10.11648/j.acm.20140305.12

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ACS Style

Boe-Shong Hong. Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics. Appl. Comput. Math. 2014, 3(5), 197-204. doi: 10.11648/j.acm.20140305.12

Copy | Download

AMA Style

Boe-Shong Hong. Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics. Appl Comput Math. 2014;3(5):197-204. doi: 10.11648/j.acm.20140305.12

Copy | Download

@article{10.11648/j.acm.20140305.12,
  author = {Boe-Shong Hong},
  title = {Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {5},
  pages = {197-204},
  doi = {10.11648/j.acm.20140305.12},
  url = {https://doi.org/10.11648/j.acm.20140305.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140305.12},
  abstract = {Scientists and engineers encounter many kinds of parabolic or hyperbolic distributed dynamics, which are often with inhomogeneous boundary conditions in practice. Boundary inhomogeneity makes the dynamics essentially nonlinear, which prevents the Hilbert space from being applied for modal decomposition and intelligent computation. Thus, this paper systematically deals with this situation via the conversion of the boundary inhomogeneity to a virtual source in conjunction with boundary homogeneity. For such a purpose, the 2D transfer-function is developed based on the Laplace-Galerkin integral transform as the main tool of this conversion. A section of numerical visualization is included to explore the topology of the virtual-source solution. Some interesting findings therein will be addressed.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics
AU  - Boe-Shong Hong
Y1  - 2014/09/20
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140305.12
DO  - 10.11648/j.acm.20140305.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 197
EP  - 204
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140305.12
AB  - Scientists and engineers encounter many kinds of parabolic or hyperbolic distributed dynamics, which are often with inhomogeneous boundary conditions in practice. Boundary inhomogeneity makes the dynamics essentially nonlinear, which prevents the Hilbert space from being applied for modal decomposition and intelligent computation. Thus, this paper systematically deals with this situation via the conversion of the boundary inhomogeneity to a virtual source in conjunction with boundary homogeneity. For such a purpose, the 2D transfer-function is developed based on the Laplace-Galerkin integral transform as the main tool of this conversion. A section of numerical visualization is included to explore the topology of the virtual-source solution. Some interesting findings therein will be addressed.
VL  - 3
IS  - 5
ER  -

Copy | Download