Publication

Analysis of a geometrical multiscale model based on the coupling of ODEs and PDEs for blood flow simulations

Alfio Quarteroni
2003
Journal Articles

Abstract

The purpose of the present article is to provide a theoretical analysis heterogeneous model coupling ordinary differential equations (ODEs) and partial differential equations (PDEs), providing a local-in-time existence result for the solution. The heterogeneous problem will actually be split into subproblems. The solution of the original problem will be regarded as the solution of a suitable fixed point problem, based on the successive solution of the subproblems. Moreover, the authors study the role of matching conditions between the two submodels for the numerical simulation.

Official source

https://infoscience.epfl.ch/entities/publication/2190b255-36ef-477c-8709-35fca86a36be

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Alfio Quarteroni
2003
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/2190b255-36ef-477c-8709-35fca86a36be

About this result

Related concepts (32)

Simulation

A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the simulation. Simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games.

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In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.

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Related publications (32)

Analysis of a geometrical multiscale model based on the coupling of ODEs and PDEs for blood flow simulations

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