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The Singular Value Expansion For Compact And Non-Compact Operators, Daniel Crane
The Singular Value Expansion For Compact And Non-Compact Operators, Daniel Crane
Dissertations, Master's Theses and Master's Reports
Given any bounded linear operator T : X → Y between separable Hilbert spaces X and Y , there exists a measure space (M, Α, µ) and isometries V : L2(M) → X, U : L2(M) → Y and a nonnegative, bounded, measurable function σ : M → [0, ∞) such that
T = UmσV †,
with mσ : L2(M ) → L2(M ) defined by mσ(f ) = σf for all f …
High Accuracy Methods And Regularization Techniques For Fluid Flows And Fluid-Fluid Interaction, Mustafa Aggul
High Accuracy Methods And Regularization Techniques For Fluid Flows And Fluid-Fluid Interaction, Mustafa Aggul
Dissertations, Master's Theses and Master's Reports
This dissertation contains several approaches to resolve irregularity issues of CFD problems, including a decoupling of non-linearly coupled fluid-fluid interaction, due to high Reynolds number. New models present not only regularize the linear systems but also produce high accurate solutions both in space and time. To achieve this goal, methods solve a computationally attractive artificial viscosity approximation of the target problem, and then utilize a correction approach to make it high order accurate. This way, they all allow the usage of legacy code | a frequent requirement in the simulation of fluid flows in complex geometries. In addition, they all …