Recent Advances in Numerical Methods and Computational Mathematics

Theory, Algorithms, and Applications in Science and Engineering

Edited by: Priya Nair · Hans Müller

ISBN: 978-1-83568-101-5 DOI: 10.12345/amse.nmcm.2023 Published: June 2023

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Type

Edited Book

ISBN

978-1-83568-101-5

DOI

10.12345/amse.nmcm.2023

Published

Jun 2023

About this Book

This edited volume brings together contributions from world-leading researchers on the forefront of numerical analysis and computational mathematics. The book covers finite element methods, spectral methods, iterative solvers, and high-performance computing techniques, with applications spanning fluid dynamics, structural mechanics, and quantum systems.

Editors

Priya Nair · Indian Institute of Technology Bombay
Hans Müller · Technical University of Berlin

Publication Details

Series: Advances in Mathematics and Scientific Engineering
Type: Edited Book
ISBN: 978-1-83568-101-5
DOI: 10.12345/amse.nmcm.2023
Year: 2023
Published: 15 Jun 2023

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01 finite element method adaptive refinement a posteriori error estimation

Adaptive Finite Element Methods for Elliptic Partial Differential Equations

Sofia Petrova*, Dmitri Volkov * corresponding author

We present a novel a posteriori error estimation framework for adaptive finite element methods applied to second-order elliptic PDEs. Our approach combines residual-based error indicators with hierarchical basis functions, achieving optimal convergence rates on both structured and unstructured meshes. Numerical experiments on benchmark problems confirm the efficiency and robustness of the proposed algorithm.

Abstract We present a novel a posteriori error estimation framework for adaptive finite element methods applied to second-order elliptic PDEs. Our approach combines residual-based error indicators with hierarchical basis functions, achieving optimal convergence rates on both structured and unstructured meshes. Numerical experiments on benchmark problems confirm the efficiency and robustness of the proposed algorithm.

02 spectral methods Navier-Stokes incompressible flow

High-Order Spectral Methods for Incompressible Navier-Stokes Equations

Amara Patel*, Ravi Sharma * corresponding author

This chapter presents high-order spectral element discretizations for the incompressible Navier-Stokes equations. We introduce a novel pressure-velocity coupling strategy that ensures inf-sup stability while maintaining spectral accuracy. The method is validated on Taylor-Green vortex and lid-driven cavity benchmark problems at moderate Reynolds numbers.

Abstract This chapter presents high-order spectral element discretizations for the incompressible Navier-Stokes equations. We introduce a novel pressure-velocity coupling strategy that ensures inf-sup stability while maintaining spectral accuracy. The method is validated on Taylor-Green vortex and lid-driven cavity benchmark problems at moderate Reynolds numbers.

03 Krylov subspace GMRES sparse linear systems

Krylov Subspace Methods for Large-Scale Sparse Linear Systems

Sofia Petrova* * corresponding author

We survey and extend Krylov subspace iterative methods for solving large-scale sparse linear systems arising in scientific computing. Special attention is paid to preconditioned GMRES, BiCGSTAB, and algebraic multigrid preconditioning. Performance comparisons on real-world application matrices from structural engineering and computational electromagnetics are provided.

Abstract We survey and extend Krylov subspace iterative methods for solving large-scale sparse linear systems arising in scientific computing. Special attention is paid to preconditioned GMRES, BiCGSTAB, and algebraic multigrid preconditioning. Performance comparisons on real-world application matrices from structural engineering and computational electromagnetics are provided.

Book Information

Series: Advances in Mathematics and Scientific Engineering
Type: Edited Book
ISBN: 978-1-83568-101-5
DOI: 10.12345/amse.nmcm.2023
Year: 2023
Published: 15 Jun 2023
Papers: 3
Language: English

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