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This book summarizes the found insights of grain growth behavior, of multidimensional decomposition for regular grids to efficiently parallelize computing and how to simulate recrystallization by coupling the finite element method with the phase-field method for microstructure texture analysis. The frame of the book is created by the phase-field method, which is the tool used in this work, to investigate microstructure phenomena.

Kornwachstum --- Wachstumsratenverteilung --- RekristallisationPhase-field --- Grain growth --- Recrystallization --- Parallelisierung --- Phasenfeld --- Growth rate distributions --- Parallelization

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This Special Issue includes papers on physical phenomena, such as wind-driven flows, coastal flooding, and turbidity currents, and modeling techniques, such as model comparison, model coupling, parallel computation, and domain decomposition. These papers illustrate the need for modeling coastal ocean flows with multiple physical processes at different scales. Additionally, these papers reflect the current status of such modeling of coastal ocean flows, and they present a roadmap with numerical methods, data collection, and artificial intelligence as future endeavors.

Technology: general issues --- History of engineering & technology --- high performance computing --- HPC --- PETSc --- parallelization --- scalability --- parallel performance --- streams --- curvilinear --- non-hydrostatic --- ocean modeling --- GCCOM --- open boundaries --- domain decomposition --- variational data assimilation --- inverse problems --- shallow water equations --- boundary conditions --- mathematical modelling --- coastal ocean modelling --- computational methods --- hydrodynamic --- modeling --- sea level rise --- mobile application --- app --- crowdsourcing --- SCHISM --- Tidewatch --- StormSense --- Catch the King --- downstream blocking --- compound flooding --- coastal storm surge and inundation --- explosive lateral flooding --- hurricane inland and upland flooding --- coastal modelling --- operational forecasting --- model evaluation --- inter-comparison --- NEMO --- FVCOM --- Ocean Protection Plan --- turbidity current --- suspended sediment --- numerical model --- Gulf of Mexico --- cold front --- Hurricane Barry --- numerical simulation --- subtidal hydrodynamics --- multi-inlet --- volume flux --- multiscale --- multiphysics --- model coupling --- data collection --- machine learning --- high performance computing --- HPC --- PETSc --- parallelization --- scalability --- parallel performance --- streams --- curvilinear --- non-hydrostatic --- ocean modeling --- GCCOM --- open boundaries --- domain decomposition --- variational data assimilation --- inverse problems --- shallow water equations --- boundary conditions --- mathematical modelling --- coastal ocean modelling --- computational methods --- hydrodynamic --- modeling --- sea level rise --- mobile application --- app --- crowdsourcing --- SCHISM --- Tidewatch --- StormSense --- Catch the King --- downstream blocking --- compound flooding --- coastal storm surge and inundation --- explosive lateral flooding --- hurricane inland and upland flooding --- coastal modelling --- operational forecasting --- model evaluation --- inter-comparison --- NEMO --- FVCOM --- Ocean Protection Plan --- turbidity current --- suspended sediment --- numerical model --- Gulf of Mexico --- cold front --- Hurricane Barry --- numerical simulation --- subtidal hydrodynamics --- multi-inlet --- volume flux --- multiscale --- multiphysics --- model coupling --- data collection --- machine learning

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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.

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