Isogeometric mixed collocation of nearly-incompressible electromechanics in finite deformations for cardiac muscle simulations

Torre, Michele; Morganti, Simone; Nitti, Alessandro; Tullio, Marco D. de; Pasqualini, Francesco S.; Reali, Alessandro

doi:10.1016/j.cma.2023.116055

Computer Methods in Applied Mechanics and Engineering

2023

DOI: 10.1016/j.cma.2023.116055

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Isogeometric mixed collocation of nearly-incompressible electromechanics in finite deformations for cardiac muscle simulations

Michele Torre

Simone Morganti

Alessandro Nitti

et al.

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Cited by 8 publications

References 45 publications

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Point collocation with mollified piecewise polynomial approximants for high‐order partial differential equations

Alfarisy,

Zuhal,

Ortiz

et al. 2024

Numerical Meth Engineering

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The solution approximation for partial differential equations (PDEs) can be substantially improved using smooth basis functions. The recently introduced mollified basis functions are constructed through mollification, or convolution, of cell‐wise defined piecewise polynomials with a smooth mollifier of certain characteristics. The properties of the mollified basis functions are governed by the order of the piecewise functions and the smoothness of the mollifier. In this work, we exploit the high‐order and high‐smoothness properties of the mollified basis functions for solving PDEs through the point collocation method. The basis functions are evaluated at a set of collocation points in the domain. In addition, boundary conditions are imposed at a set of boundary collocation points distributed over the domain boundaries. To ensure the stability of the resulting linear system of equations, the number of collocation points is set larger than the total number of basis functions. The resulting linear system is overdetermined and is solved using the least square technique. The presented numerical examples confirm the convergence of the proposed approximation scheme for Poisson, linear elasticity, and biharmonic problems. We study in particular the influence of the mollifier and the spatial distribution of the collocation points.

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Point collocation with mollified piecewise polynomial approximants for high‐order partial differential equations

Alfarisy,

Zuhal,

Ortiz

et al. 2024

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

An isogeometric approach to coupled thermomechanics in 3D via hierarchical adaptivity

Carraturo,

Torre,

Giannelli

et al. 2024

Computers & Mathematics with Applications

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An efficient displacement-based isogeometric formulation for geometrically exact viscoelastic beams

Ferri,

Ignesti,

Marino

2023

Computer Methods in Applied Mechanics and Engineering

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Isogeometric mixed collocation of nearly-incompressible electromechanics in finite deformations for cardiac muscle simulations

Cited by 8 publications

References 45 publications

Point collocation with mollified piecewise polynomial approximants for high‐order partial differential equations

Point collocation with mollified piecewise polynomial approximants for high‐order partial differential equations

An isogeometric approach to coupled thermomechanics in 3D via hierarchical adaptivity

An efficient displacement-based isogeometric formulation for geometrically exact viscoelastic beams

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