Automation of Error Control with Application to Fluid-Structure Interaction in Biomedicine.

Computer simulation is an important tool in many areas of science. Increasingly complex mathematical models are being solved in large computer simulations, complementing and sometimes replacing traditional experimental techniques as the main tool of scien tific investigation. In any such computer simulation, it is pivotal that the quality of the computed solution may be determined. However, the assessment of the quality of a computed solution is challenging, both mathematically and computationally. As a co nsequence, the quality of the solution must often be assessed manually by the scientist or engineer running the simulation. This is unreliable as well as time-consuming, and it effectively prevents computer simulation from realizing its full potential as a standard tool in science and industry. The aim of the proposed research is to develop a general methodology for automated computation and error control, with special emphasis on fluid-structure interaction problems in biomedicine. The aim is also to re alize the methodology in free software components that are accessible to practitioners, including medical doctors. Currently, no such tools exist and the relevance and potential impact of the proposed research is therefore very large. The proposed resear ch has a broad spectrum and is expected to produce concrete results that include a general mathematical methodology for automated error control, software components implementing the methodology and increased knowledge for a set of challenging key applicat ions in biomedicine, including the simulation of turbulent flow through the aortic valve, pulmonary support by forced ventilation and diagnosis of stenosis by noninvasive acoustic measurement. The research will be carried out in collaboration with resear ch groups in Norway, Sweden, the Netherlands and the USA.