Fast solvers for flow problems

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This work covers a range of advanced numerical methods and techniques for solving complex fluid dynamics and transport equations. It introduces a hierarchical basis multigrid method tailored for unstructured grids and explores structured adaptive finite-volume multigrid approaches for compressible flows. The text addresses the solution of nonlinear equations related to nondifferentiable mappings and presents finite element solutions for incompressible Navier-Stokes equations on anisotropically refined meshes. A robust multigrid method for convection-diffusion problems is discussed, along with a fast solver designed for gas flow networks. The design of piecewise uniform meshes for advection-dominated transport equations is examined, alongside numerical simulations of three-dimensional non-stationary compressible flows in complex geometries. Coupled transient problems on MIMD parallel systems are also analyzed. The work includes fast solvers for coupled FEM-BEM equations and discusses numerical simulations of compressible Navier-Stokes equations with nonequilibrium chemistry. Additionally, it presents preconditioned CG-like methods and defect correction techniques for steady incompressible Navier-Stokes equations, along with domain decomposition methods for singularly perturbed elliptic problems. The text highlights parallel subspace decomposition methods for elliptic and hyperbolic systems, implicit time-discretization techni