کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4499912 1624008 2016 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Stability analysis of the POD reduced order method for solving the bidomain model in cardiac electrophysiology
موضوعات مرتبط
علوم زیستی و بیوفناوری علوم کشاورزی و بیولوژیک علوم کشاورزی و بیولوژیک (عمومی)
پیش نمایش صفحه اول مقاله
Stability analysis of the POD reduced order method for solving the bidomain model in cardiac electrophysiology
چکیده انگلیسی

In this paper we show the numerical stability of the Proper Orthogonal Decomposition (POD) reduced order method used in cardiac electrophysiology applications. The difficulty of proving the stability comes from the fact that we are interested in the bidomain model, which is a system of degenerate parabolic equations coupled to a system of ODEs representing the cell membrane electrical activity. The proof of the stability of this method is based on a priori estimates controlling the gap between the reduced order solution and the Galerkin finite element one. We present some numerical simulations confirming the theoretical results. We also combine the POD method with a time splitting scheme allowing a faster solving of the bidomain problem and show numerical results. Finally, we conduct numerical simulation in 2D illustrating the stability of the POD method in its sensitivity to the ionic model parameters. We also perform 3D simulation using a massively parallel code. We show the computational gain using the POD reduced order model. We also show that this method has a better scalability than the full finite element method.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Mathematical Biosciences - Volume 272, February 2016, Pages 81–91
نویسندگان
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