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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.23 No.4
- 발행연도
- 2019.12
- 수록면
- 301 - 327 (27page)
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초록· 키워드
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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.
목차
ABSTRACT
1. INTRODUCTION
2. PROPER ORTHOGONAL DECOMPOSITION
3. POD COLLOCATION FOR HYPERBOLIC CONSERVATION LAWS
4. POST-PROCESSING OF SAMPLE SOLUTIONS
5. NUMERICAL EXAMPLES
6. CONCLUSION
REFERENCES
참고문헌 (26)
참고문헌 신청
P. Benner / 2015 / Special Issue: Model Order Reduction of Parameterized Systems / Adv. Comput. Math 41
G. Berkooz / 1993 / The proper orthogonal decomposition in the analysis of turbulent flows / Ann. Rev. Fluid Mech 25:539~575
J. Burkardt / 2006 / Centroidal Voronoi tessellation-based reduced-order modeling of complex systems / SIAM J. Sci. Comput 28(2):459~484
J. Burkardt / 2006 / POD and CVT-based reduced-order modeling of Navier-Stokes flows / Comput. Meth. Appl. Mech. Eng 196:337~355
Q. Du / 1999 / Centroidal Voronoi tessellations: applications and algorithms / SIAM Rev 41(4):637~676
G. Berkooz / 1993 / The proper orthogonal decomposition in the analysis of turbulent flows / Ann. Rev. Fluid Mech 25:539~575
J. Burkardt / 2006 / Centroidal Voronoi tessellation-based reduced-order modeling of complex systems / SIAM J. Sci. Comput 28(2):459~484
J. Burkardt / 2006 / POD and CVT-based reduced-order modeling of Navier-Stokes flows / Comput. Meth. Appl. Mech. Eng 196:337~355
Q. Du / 1999 / Centroidal Voronoi tessellations: applications and algorithms / SIAM Rev 41(4):637~676
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UCI(KEPA) : I410-ECN-0101-2020-410-000107357