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Introduction to Numerical Methods for Variational Problems / / by Hans Petter Langtangen, Kent-Andre Mardal
| Introduction to Numerical Methods for Variational Problems / / by Hans Petter Langtangen, Kent-Andre Mardal |
| Autore | Langtangen Hans Petter |
| Edizione | [1st ed. 2019.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 |
| Descrizione fisica | 1 online resource (XVI, 395 p. 88 illus., 76 illus. in color.) |
| Disciplina | 515.64 |
| Collana | Texts in Computational Science and Engineering |
| Soggetto topico |
Computer mathematics
Computational Mathematics and Numerical Analysis |
| ISBN | 3-030-23788-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Quick overview of the finite element method -- Function approximation by global functions -- Function approximation by finite elements -- Variational formulations with global elements -- Variational formulations with finite elements -- Time-dependent variational forms -- Variational forms for systems of PDEs -- Nonlinear Problems -- Variational forms for linear systems -- Useful formulas. |
| Record Nr. | UNINA-9910349318903321 |
Langtangen Hans Petter
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Modeling excitable tissue : the EMI framework / / editors, Aslak Tveito, Kent-Andre Mardal, Marie E. Rognes
| Modeling excitable tissue : the EMI framework / / editors, Aslak Tveito, Kent-Andre Mardal, Marie E. Rognes |
| Autore | Tveito Aslak |
| Edizione | [1st edition 2021.] |
| Pubbl/distr/stampa | Springer Nature, 2021 |
| Descrizione fisica | 1 online resource (XVII, 100 p. 25 illus. in color.) |
| Disciplina | 570.285 |
| Collana | Reports on Computational Physiology |
| Soggetto topico |
Bioinformatics
Cell physiology Computational biology Excitation (Physiology) - Mathematical models Mathematical models |
| Soggetto non controllato |
Mathematical and Computational Biology
Applications of Mathematics Mathematical Modeling and Industrial Mathematics applied mathematics scientific computing computational physiology finite element methods cardiac modelling biomechanics numerical methods preconditioning open access Maths for scientists Mathematical modelling Maths for engineers |
| ISBN | 3-030-61157-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Derivation of a cell-based mathematical model of excitable cells -- A cell-based model for ionic electrodiffusion in excitable tissue -- Modeling cardiac mechanics on a subcellular scale -- Operator splitting and finite difference schemes for solving the EMI model -- Solving the EMI equations using finite element methods -- Iterative solvers for EMI models -- Improving neural simulations with the EMI model -- Index. |
| Record Nr. | UNINA-9910424947903321 |
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Tveito Aslak
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| Springer Nature, 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Modeling excitable tissue : the EMI framework / / editors, Aslak Tveito, Kent-Andre Mardal, Marie E. Rognes
| Modeling excitable tissue : the EMI framework / / editors, Aslak Tveito, Kent-Andre Mardal, Marie E. Rognes |
| Autore | Tveito Aslak |
| Edizione | [1st edition 2021.] |
| Pubbl/distr/stampa | Springer Nature, 2021 |
| Descrizione fisica | 1 online resource (XVII, 100 p. 25 illus. in color.) |
| Disciplina | 570.285 |
| Collana | Reports on Computational Physiology |
| Soggetto topico |
Bioinformatics
Cell physiology Computational biology Excitation (Physiology) - Mathematical models Mathematical models |
| Soggetto non controllato |
Mathematical and Computational Biology
Applications of Mathematics Mathematical Modeling and Industrial Mathematics applied mathematics scientific computing computational physiology finite element methods cardiac modelling biomechanics numerical methods preconditioning open access Maths for scientists Mathematical modelling Maths for engineers |
| ISBN | 3-030-61157-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Derivation of a cell-based mathematical model of excitable cells -- A cell-based model for ionic electrodiffusion in excitable tissue -- Modeling cardiac mechanics on a subcellular scale -- Operator splitting and finite difference schemes for solving the EMI model -- Solving the EMI equations using finite element methods -- Iterative solvers for EMI models -- Improving neural simulations with the EMI model -- Index. |
| Record Nr. | UNISA-996466563303316 |
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Tveito Aslak
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| Springer Nature, 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Quantitative Approaches to Microcirculation : Mathematical Models, Computational Methods and Data Analysis
| Quantitative Approaches to Microcirculation : Mathematical Models, Computational Methods and Data Analysis |
| Autore | Linninger Andreas |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing AG, , 2024 |
| Descrizione fisica | 1 online resource (0 pages) |
| Altri autori (Persone) |
MardalKent-Andre
ZuninoPaolo |
| Collana | SEMA SIMAI Springer Series |
| ISBN | 3-031-58519-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Mathematical Models of the Cerebral Microcirculation in Health and Pathophysiology -- 1 Introduction -- 2 Methodology -- 3 Applications -- 4 Future Directions -- 5 Conclusions -- References -- A Computational Model of the Tumor Microenvironment Applied to Fractionated Radiotherapy -- 1 Introduction -- 2 An Oxygen Transport Model Coupled to Radiotherapy -- 2.1 A Mixed-Dimensional Oxygen Transport Model -- 2.2 Constitutive Laws of the Oxygen Transport Model -- 2.3 The Linear-Quadratic Radiobiological Model -- 2.4 Coupling the Oxygen Transport and the Radiobiological Models -- 2.5 Numerical Methods -- 3 Numerical Simulations of the Interaction of Radiotherapy and the Tumor Microenvironment -- 3.1 The Effect of Fractionated Radiotherapy -- 3.2 The Effect of Reoxygenation After Radiotherapy -- 3.3 The Effect of Vascular Modifications Due to Radiotherapy -- 4 Discussion and Conclusions -- References -- Microvascular Modeling for Medical Imaging and ToxicityAssessment -- 1 Introduction -- 2 Methods: Key Concepts and Equations -- 2.1 Continuum Mechanics of Fluids: The Balance of Mass and Momentum -- 2.1.1 Mass Balance -- 2.1.2 Momentum Balance -- 2.1.3 System of Equations of a Continuum -- 2.2 Hemodynamics Modeling -- 2.2.1 The Navier-Stokes Equations -- 2.2.2 The (Hagen-)Poiseuille Flow Model -- 2.3 Viscosity Law -- 2.4 Transport in a Vascularized Tissue -- 2.4.1 Multi-Components, Single Phase Models -- 2.4.2 Multi-Components, Multi-Phases Models -- 2.4.3 Compartment Models -- 2.5 Vascular Networks -- 2.5.1 Geometry -- 2.5.2 Hemodynamics in Vessel Networks -- 2.5.3 Transport -- 3 Results -- 3.1 Case 1: Vascularized Tumor -- 3.1.1 Motivations -- 3.1.2 Specific Equations and Boundary Conditions -- 3.1.3 Numerical Methods -- 3.1.4 Results -- 3.2 Case 2: Lobule -- 3.2.1 Specific Equations and Boundary Conditions.
3.2.2 Results -- 3.3 Case 3: Toxicity -- 3.3.1 Specific Equations and Boundary Conditions -- 3.3.2 Results -- 4 Discussion -- 4.1 Strengths and Limitations of These Approaches -- 4.2 Similarities and Differences in the Three Cases -- 5 Conclusion and Perspectives -- Appendix -- References -- Finite Element Software and Performance for Network Models with Multipliers -- 1 Introduction -- 2 A Minimal Mixed-Dimensional Model: Hydraulic Networks with Multipliers -- 2.1 Mathematical Model -- 2.2 A Mixed Finite Element Method -- 3 Software Components and Implementation -- 3.1 Mixed-Domain Abstractions and Algorithms in FEniCS and FEniCSx -- 3.1.1 Submeshes -- 3.1.2 Mixed-Domain Finite Element Kernel Generation -- 3.1.3 Mixed-Domain Assembly -- 3.2 Implementation of the Hydraulic Network Solver -- 4 Results -- 4.1 Network Code Generation and Assembly in FEniCS vs FEniCSx -- 4.2 FEniCSx Performance on Larger Networks -- 5 Conclusions, Limitations, and Further Work -- References -- A Fast-Fourier Preconditioned Schur Complement Method for the Simulation of Cerebrocortical Oxygen Supply -- 1 Introduction -- 2 Models and Methods -- 2.1 Overview -- 2.2 Graph Representation and Discretization of Vascular and Tissue Domains -- 2.3 Simulation of Blood Flow in the Vascular Network -- 2.4 Oxygen Convection and Mass Transfer in the Vascular Domain -- 2.4.1 The Connectivity Matrix of a Graph -- 2.4.2 The Convection Matrices -- 2.4.3 Fast Inversion of the Convection Matrices -- 2.4.4 Dissociation of Oxygen from RBCs to Plasma -- 2.4.5 The Connectivity Matrix of the Domain Coupling -- 2.5 Oxygen Metabolism and Diffusion in the Tissue Domain -- 2.5.1 The Graph Laplacian -- 2.5.2 Fast Inversion of the Graph Laplacian with Dirichlet Boundary Conditions -- 2.5.3 Metabolism in the Tissue -- 2.6 Steady-State: Schur Complement of the Linearized System -- 2.6.1 The Newton Step. 2.6.2 The Schur Complement System -- 2.6.3 Preconditioning the Schur Complement System -- 2.7 The Dynamic Case -- 2.7.1 The Newton Step -- 2.7.2 The Preconditioned Schur Complement System -- 2.7.3 Summary of Method -- 3 Application to Massive Steady-State Oxygen Exchange Simulation in the Cerebral Cortex -- 3.1 Pure Diffusion of an Ideal Solute -- 3.2 Idealized Exchange of Oxygen Across the Blood Brain Barrier (Linear Mass Transfer) -- 3.3 Cortical Oxygen Extraction with Nonlinear Dissociation Kinetics -- 4 Discussion -- 5 Conclusions -- Appendix 1: Discretization of the Continuous Problem -- Appendix 2: Dependence of the DST on Domain Side Length -- Appendix 3: Dynamic Oxygen Simulation for a Single Capillary -- References -- Robust Preconditioning of Mixed-Dimensional PDEs on 3d-1d Domains Coupled with Lagrange Multipliers -- 1 Introduction -- 2 Mathematical Formulation of the 3d-1d Coupled Problem -- 2.1 The Stability of the Continuous Problem -- 2.2 Numerical Evidence About Preconditioning the Mixed-Dimensional Problems -- 3 Definition of a Preconditioner for the 3d-1d Problem: Performances and Drawbacks -- 4 The Role of the Inner Radius on Mixed-Dimensional Problems -- 4.1 The 2d-1d Formulation for the Perforated Domain Problem -- 4.2 Numerical Results About the 2d-1d Formulation -- 4.3 The 2d-0d Formulation for the Perforated Domain Problem -- 5 Conclusion -- Appendix -- Numerical Experiments for Square-Shaped Inclusion -- Numerical Experiments for Layered Mesh -- Numerical Experiments for P2-P1 Discretization -- References -- Numerical Approaches for Multiphase Microfluids -- 1 Introduction -- 2 Fluid/Fluid Interaction -- 2.1 Tangent of Hyperbola Interface Capturing (THINC) Method -- 2.2 Pressure Poisson Equation -- 2.3 Applications in Microfluidics -- 2.4 Emulsions Effective Viscosity -- 3 Fluid/Structure Interaction: The dynamic-IB Approach. 3.1 Fluid Evolution on Ω -- 3.2 Dirichlet Boundary Condition on ∂Ω -- 3.3 Evolution of M(t) -- 3.4 Dirichlet Boundary Conditions on M(t) -- 3.5 Strength and Limitations of the Dynamic-IB Approach -- 4 Conclusive Remarks -- References -- Application of the Zenger Correction to an Elliptic PDE with Dirac Source Term -- 1 Introduction -- 2 Model Problem -- 3 Iterative Solution Scheme -- 4 Application of the Zenger Correction -- 5 Numerical Tests -- 5.1 Local Convergence Behavior -- 5.2 Accurate Computation of the Exchange Term -- 5.3 Convergence of the Iterative Solution Scheme -- 6 Conclusions and Outlook -- References. |
| Record Nr. | UNINA-9910874675503321 |
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Linninger Andreas
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| Cham : , : Springer International Publishing AG, , 2024 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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