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Volume 13 (2022): Issue 1 (January 2022)

Volume 12 (2021): Issue 1 (January 2021)

Volume 11 (2020): Issue 1 (January 2020)

Volume 10 (2019): Issue 2 (January 2019)
Special Issue on Mathematical Models and Methods in Biology, Medicine and Physiology. Guest Editors: Michele Piana, Luigi Preziosi

Volume 10 (2019): Issue 1 (February 2019)

Volume 9 (2018): Issue 2 (December 2018)
Special Issue on Mathematical modelling for complex systems: multi-agents methods. Guest Editor: Elena De Angelis

Volume 9 (2018): Issue 1 (February 2018)

Volume 8 (2017): Issue 1 (March 2017)

Volume 7 (2016): Issue 3 (September 2016)
"Special Issue on New Trends in Semi-Lagrangian Methods, Guest Editors: Luca Bonaventura, Maurizio Falcone and Roberto Ferretti

Volume 7 (2016): Issue 2 (June 2016)
Special Issue on Constitutive Equations for Heat Conduction in Nanosystems and Non-equilibrium Processes. Guest Editors: Vito Antonio Cimmelli and David Jou

Volume 7 (2016): Issue 1 (January 2016)
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Journal Details
Format
Journal
eISSN
2038-0909
First Published
15 Dec 2014
Publication timeframe
1 time per year
Languages
English

Search

Volume 13 (2022): Issue 1 (January 2022)

Journal Details
Format
Journal
eISSN
2038-0909
First Published
15 Dec 2014
Publication timeframe
1 time per year
Languages
English

Search

3 Articles
access type Open Access

Polynomial mapped bases: theory and applications

Published Online: 16 May 2022
Page range: 1 - 9

Abstract

Abstract

In this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-imaging reconstruction. The method relies on polynomial mapped bases allowing, for instance, to incorporate data or function discontinuities in a suitable mapping function. The new technique substantially mitigates the Runge’s and Gibbs effects.

Keywords

  • mapped basis
  • Gibbs phenomenon
  • Runge’s phenomenon
  • fake nodes
access type Open Access

Recent Trends on Nonlinear Filtering for Inverse Problems

Published Online: 22 May 2022
Page range: 10 - 20

Abstract

Abstract

Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the original method and discuss recent developments in particular in view of the limit for infinitely particles and extensions towards stability analysis and multi–objective optimization. We illustrate the performance of the method by using test inverse problems from the literature.

Keywords

  • Ensemble Kalman inversion
  • nonlinear filtering methods
  • inverse problems
  • multi-objective optimization
  • stability analysis
access type Open Access

High order Finite Difference/Discontinuous Galerkin schemes for the incompressible Navier-Stokes equations with implicit viscosity

Published Online: 27 Jun 2022
Page range: 21 - 38

Abstract

Abstract

In this work we propose a novel numerical method for the solution of the incompressible Navier-Stokes equations on Cartesian meshes in 3D. The semi-discrete scheme is based on an explicit discretization of the nonlinear convective flux tensor and an implicit treatment of the pressure gradient and viscous terms. In this way, the momentum equation is formally substituted into the divergence-free constraint, thus obtaining an elliptic equation on the pressure which eventually maintains at the discrete level the involution on the divergence of the velocity field imposed by the governing equations. This makes our method belonging to the class of so-called structure-preserving schemes. High order of accuracy in space is achieved using an efficient CWENO reconstruction operator that is exploited to devise a conservative finite difference scheme for the convective terms. Implicit central finite differences are used to remove the numerical dissipation in the pressure gradient discretization. To avoid the severe time step limitation induced by the viscous eigenvalues related to the parabolic terms in the governing equations, we propose to devise an implicit local discontinuous Galerkin (DG) solver. The resulting viscous sub-system is symmetric and positive definite, therefore it can be efficiently solved at the aid of a matrix-free conjugate gradient method. High order in time is granted by a semi-implicit IMEX time stepping technique. Convergence rates up to third order of accuracy in space and time are proven, and a suite of academic benchmarks is shown in order to demonstrate the robustness and the validity of the novel schemes, especially in the context of high viscosity coefficients.

Keywords

  • incompressible Navier-Stokes
  • IMEX schemes
  • implicit viscosity terms
  • high order in space and time
3 Articles
access type Open Access

Polynomial mapped bases: theory and applications

Published Online: 16 May 2022
Page range: 1 - 9

Abstract

Abstract

In this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-imaging reconstruction. The method relies on polynomial mapped bases allowing, for instance, to incorporate data or function discontinuities in a suitable mapping function. The new technique substantially mitigates the Runge’s and Gibbs effects.

Keywords

  • mapped basis
  • Gibbs phenomenon
  • Runge’s phenomenon
  • fake nodes
access type Open Access

Recent Trends on Nonlinear Filtering for Inverse Problems

Published Online: 22 May 2022
Page range: 10 - 20

Abstract

Abstract

Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the original method and discuss recent developments in particular in view of the limit for infinitely particles and extensions towards stability analysis and multi–objective optimization. We illustrate the performance of the method by using test inverse problems from the literature.

Keywords

  • Ensemble Kalman inversion
  • nonlinear filtering methods
  • inverse problems
  • multi-objective optimization
  • stability analysis
access type Open Access

High order Finite Difference/Discontinuous Galerkin schemes for the incompressible Navier-Stokes equations with implicit viscosity

Published Online: 27 Jun 2022
Page range: 21 - 38

Abstract

Abstract

In this work we propose a novel numerical method for the solution of the incompressible Navier-Stokes equations on Cartesian meshes in 3D. The semi-discrete scheme is based on an explicit discretization of the nonlinear convective flux tensor and an implicit treatment of the pressure gradient and viscous terms. In this way, the momentum equation is formally substituted into the divergence-free constraint, thus obtaining an elliptic equation on the pressure which eventually maintains at the discrete level the involution on the divergence of the velocity field imposed by the governing equations. This makes our method belonging to the class of so-called structure-preserving schemes. High order of accuracy in space is achieved using an efficient CWENO reconstruction operator that is exploited to devise a conservative finite difference scheme for the convective terms. Implicit central finite differences are used to remove the numerical dissipation in the pressure gradient discretization. To avoid the severe time step limitation induced by the viscous eigenvalues related to the parabolic terms in the governing equations, we propose to devise an implicit local discontinuous Galerkin (DG) solver. The resulting viscous sub-system is symmetric and positive definite, therefore it can be efficiently solved at the aid of a matrix-free conjugate gradient method. High order in time is granted by a semi-implicit IMEX time stepping technique. Convergence rates up to third order of accuracy in space and time are proven, and a suite of academic benchmarks is shown in order to demonstrate the robustness and the validity of the novel schemes, especially in the context of high viscosity coefficients.

Keywords

  • incompressible Navier-Stokes
  • IMEX schemes
  • implicit viscosity terms
  • high order in space and time

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