Objective
In this project we aim at addressing mathematical and numerical methods based on virtual controls for the coupling of heterogeneous problems described by partial differential equations.
These problems arise in many practical applications. For example, whenever different phenomena have to be taken into account in two or more subregions of the computational domain, or when, for the description and simulation of complex physical phenomena, combinations of hierarchical mathematical models are set up with the aim of reducing the computational complexity.
In both cases, we have to study a multiphysics problem, i.e. a system of heterogeneous problems, where different kind of differential problems are defined in different subregions (either disjoint or overlapping) of the original computational domain.
Virtual control is a powerful technique based on the optimal control theory that has been introduced in domain decomposition method with overlapping subdomains to treat homogeneous problems, either elliptic and parabolic.
The basic idea of this approach consists in introducing suitable functions called ``virtual'' controls which play the role of unknown boundary data on the interfaces of the decomposition and in minimizing in a suitable norm the difference between the solutions of the subproblems on the overlap.
In this project we aim at extending the virtual control method for a class of heterogeneous problems considering both analytical and computational aspects. In particular, we will characterize suitable functionals to be minimized on the overlapping regions in order to ensure both the well-posedness of the problem and a correct description of the physical phenomena of interest. Moreover, we will focus on the development of effective numerical methods and preconditioning techniques for the solution of the optimality systems arising from this approach.
Finally, we will consider several problems of practical interest to validate the methodology that we propose.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
- natural sciences computer and information sciences computational science multiphysics
- natural sciences mathematics applied mathematics numerical analysis
- natural sciences mathematics applied mathematics mathematical model
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP7-PEOPLE-2011-CIG
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Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
MC-CIG - Support for training and career development of researcher (CIG)
Coordinator
08034 Barcelona
Spain
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.