Abstract
In this paper we introduce a new computational method for solving the diffusion equation. In particular, we construct a “generalized” state-space system and compute the impulse response of an equivalent truncated state-space system. In this effort, we use a 3D finite element method (FEM) to obtain the state-space system. We then use the Arnoldi iteration to approximate the state impulse response by projecting on the dominant controllable subspace. The idea exploited here is the approximation of the impulse response of the linear system. We study the homogeneous and heterogeneous cases and discuss the approximation error. Finally, we compare our computational results to our experimental setup.
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This research was supported by the Central Research Laboratory, Hamamatsu Photonics K.K., 5000 Hirakuchi, Hamakita 434, Japan.
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Su, Q., Syrmos, V.L. & Yun, D.Y.Y. A numerical algorithm for the diffusion equation using 3D FEM and the Arnoldi method. Circuits Systems and Signal Process 18, 291–314 (1999). https://doi.org/10.1007/BF01225699
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DOI: https://doi.org/10.1007/BF01225699