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Finite Difference Computing with PDEs: A Modern Software Approach

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Book Series: Texts in Computational Science and Engineering ISSN: 1611-0994 / 2197-179X ISBN: 9783319554556 9783319554563 Year: Pages: 507 DOI: https://doi.org/10.1007/978-3-319-55456-3 Language: English
Publisher: Springer Nature
Subject: Computer Science
Added to DOAB on : 2017-11-24 13:03:18
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This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Microwave Imaging and Electromagnetic Inverse Scattering Problems

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ISBN: 9783039219506 / 9783039219513 Year: Pages: 170 DOI: 10.3390/books978-3-03921-951-3 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2020-06-09 16:38:57
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Microwave imaging techniques allow for the development of systems that are able to inspect, identify, and characterize in a noninvasive fashion under different scenarios, ranging from biomedical to subsurface diagnostics as well as from surveillance and security applications to nondestructive evaluation. Such great opportunities, though, are actually severely limited by difficulties arising from the solution of the underlying inverse scattering problem. As a result, ongoing research efforts in this area are devoted to developing inversion strategies and experimental apparatus so that they are as reliable and accurate as possible with respect to reconstruction capabilities and resolution performance, respectively. The intent of this Special Issue is to present the experiences of leading scientists in the electromagnetic inverse scattering community, as well as to serve as an assessment tool for people who are new to the area of microwave imaging and electromagnetic inverse scattering problems.

Advanced Numerical Methods in Applied Sciences

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ISBN: 9783038976660 9783038976677 Year: Pages: 306 DOI: 10.3390/books978-3-03897-667-7 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-06-26 08:44:06
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The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.

Keywords

time fractional differential equations --- mixed-index problems --- analytical solution --- asymptotic stability --- conservative problems --- Hamiltonian problems --- energy-conserving methods --- Poisson problems --- Hamiltonian Boundary Value Methods --- HBVMs --- line integral methods --- constrained Hamiltonian problems --- Hamiltonian PDEs --- highly oscillatory problems --- boundary element method --- finite difference method --- floating strike Asian options --- continuous geometric average --- barrier options --- isogeometric analysis --- adaptive methods --- hierarchical splines --- THB-splines --- local refinement --- linear systems --- preconditioners --- Cholesky factorization --- limited memory --- Volterra integral equations --- Volterra integro–differential equations --- collocation methods --- multistep methods --- convergence --- B-spline --- optimal basis --- fractional derivative --- Galerkin method --- collocation method --- spectral (eigenvalue) and singular value distributions --- generalized locally Toeplitz sequences --- discretization of systems of differential equations --- higher-order finite element methods --- discontinuous Galerkin methods --- finite difference methods --- isogeometric analysis --- B-splines --- curl–curl operator --- time harmonic Maxwell’s equations and magnetostatic problems --- low rank completion --- matrix ODEs --- gradient system --- ordinary differential equations --- Runge–Kutta --- tree --- stump --- order --- elementary differential --- edge-histogram --- edge-preserving smoothing --- histogram specification --- initial value problems --- one-step methods --- Hermite–Obreshkov methods --- symplecticity --- B-splines --- BS methods --- hyperbolic partial differential equations --- high order discontinuous Galerkin finite element schemes --- shock waves and discontinuities --- vectorization and parallelization --- high performance computing --- generalized Schur algorithm --- null-space --- displacement rank --- structured matrices --- stochastic differential equations --- stochastic multistep methods --- stochastic Volterra integral equations --- mean-square stability --- asymptotic stability --- numerical analysis --- numerical methods --- scientific computing --- initial value problems --- one-step methods --- Hermite–Obreshkov methods --- symplecticity --- B-splines --- BS methods

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