A gradient based resolution strategy for a PDE-constrained optimization approach for 3D-1D coupled problems

Berrone, Stefano; Grappein, Denise; Scialò, Stefano; Vicini, Fabio

doi:10.1007/s13137-021-00192-0

Cited by 7 publications

(2 citation statements)

References 21 publications

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“…Indeed, the treatment of such narrow and elongated regions as one-dimensional manifolds reduces the overhead in simulations related to the generation of a computational mesh inside the inclusions. On the other hand, the mathematical formulation of 3D-1D coupled problems requires non standard approaches, and specialized numerical schemes are needed to correctly account for the presence of singularities [8,9,7,12,3]. The use of a 3D mesh non conforming to the 1D domains is quite a standard in the available approaches, but, in some cases, sub-optimal convergence rates are observed unless adaptive refinement close to the singularity is used, see e.g.…”

Section: Introductionmentioning

confidence: 99%

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Extended Finite Elements for 3D-1D coupled problems via a PDE-constrained optimization approach

Grappein¹,

Scialò²,

Vicini³

2022

Preprint

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In this work we propose the application of the eXtended Finite Element Method (XFEM) to the simulation of coupled elliptic problems on 3D and 1D domains, arising from the application of geometrical reduction models to fully three dimensional problems with cylindrical, or nearly cylindrical, inclusions with small radius. In this context, the use of non conforming meshes is widely adopted, even if, due to the presence of singular source terms for the 3D problems, mesh adaptation near the embedded 1D domains may be necessary to improve solution accuracy and to recover optimal convergence rates. The XFEM are used here as an alternative to mesh adaptation. The choice of a suitable enrichment function is presented and an effective quadrature strategy is proposed. Numerical tests show the effectiveness of the approach.

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Section: Introductionmentioning

confidence: 99%

“…The formulation here shortly described can be generalized to different boundary conditions, to multiple intersecting segments [3] and to different interface conditions [2].…”

Section: Introductionmentioning

confidence: 99%

Extended Finite Elements for 3D-1D coupled problems via a PDE-constrained optimization approach

Grappein¹,

Scialò²,

Vicini³

2022

Preprint

Self Cite

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Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains

Mel’nyk,

Rohde

2024

Nonlinear Differ. Equ. Appl.

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The aim of the paper is to construct and justify asymptotic approximations for solutions to quasilinear convection–diffusion problems with a predominance of nonlinear convective flow in a thin cylinder, where an inhomogeneous nonlinear Robin-type boundary condition involving convective and diffusive fluxes is imposed on the lateral surface. The limit problem for vanishing diffusion and the cylinder shrinking to an interval is a nonlinear first-order conservation law. For a time span that allows for a classical solution of this limit problem corresponding uniform pointwise and energy estimates are proven. They provide precise model error estimates with respect to the small parameter that controls the double viscosity-geometric limit. In addition, other problems with more higher Péclet numbers are also considered.

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A binary tournament competition algorithm for solving partial differential equation constrained optimization via finite element method

Kumar

Mahato

Bhunia

2022

Applied Soft Computing

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A gradient based resolution strategy for a PDE-constrained optimization approach for 3D-1D coupled problems

Cited by 7 publications

References 21 publications

Extended Finite Elements for 3D-1D coupled problems via a PDE-constrained optimization approach

Extended Finite Elements for 3D-1D coupled problems via a PDE-constrained optimization approach

Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains

A binary tournament competition algorithm for solving partial differential equation constrained optimization via finite element method

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