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Istanbul is the most important city of Turkey in the view of economical, social and cultural aspects. Because of the active faults in the Sea of Marmara, there is always an expectation of an important earthquake that will be harmful for the city and also for the other big cities that are located around the Sea of Marmara such as Bursa, İzmit, Tekirdağ and Yalova. In addition to the earthquake, a tsunami which occurs in the Sea of Marmara can also be a very destructive hazard for Istanbul and other cities around the Sea of Marmara. There are many tsunamis that happened in the Sea of Marmara in the history. The main reason of these tsunamis is the slumps and the landslides that were triggered by an earthquake. One of the most important reasons of the tsunamis on the earth is the submarine landslides. Movement at the sea bottom stirs the above water mass. This causes tsunami waves and these waves damage the coastal areas seriously. The aim of this study is to find the maximum wave heights of possible tsunamis around Tuzla coasts using different scenarios. A submarine landslide that may be occurred after an earthquake or because of any other reason in the Sea of Marmara at the region near to northeast Marmara coasts is taken as the reason of the tsunami in the simulations that are performed in the study. As the solution method, one hybrid method was developed. The main objective of this method is to combine an analytical solution presenting near-field tsunami amplitudes above the submarine mass failure with a numerical solution indicating the tsunami amplitudes in the coastal regions. An analytical model that is frequently used in the literature was applied to find the amplitudes of tsunami waves at the surface of Sea of Marmara above the submarine landslide region. These tsunami waves will be directly affected from the water depth of the Sea of Marmara. It will be also affected by the shore profile when traveling to the coasts. Because of this reason, a computational fluid dynamics model which is based on finite elements method is used in the regions that are very close to the coasts. The model solves the Navier-Stokes equations. Analytical and numerical models were used together in this study. The analytical model is used from the submarine up to sea surface and the numerical model is used for modeling of the movement of the tsunami waves at the sea surfaces. In the border of two models the outputs of analytical model is used as the inputs of numerical model that means the initial and boundary conditions of numerical model is obtained from the analytical model.… [ABSTRACT FROM AUTHOR]

Multiple large linear systems with a same coefficient matrix but different right-hand side vectors arise in several problems of engineering such as in solution of Navier-Stokes equations in different directions (Dinler, 2007). Moreover, seeking an optimum or a special solution of a multi-dimensional PDE with a parameter-dependent moving source term or changing force term, or variable boundary conditions requires repeated solution of this PDE with changing values of the parameter. In that case, we need to solve multiple large linear systems with a same coefficient matrix but different right-hand side vectors. To solve these large block linear systems efficiently, block Krylov subspace methods (in short block Kylov methods) are an important tool. Krylov subspace methods are projection methods that search the solution of a linear system iteratively in the Krylov subspace. Comparing with direct methods such as Gauss elimination or LU decomposition, direct methods are prohibitive to solve large linear systems however Krylov subspace methods are efficient. Moreover in several engineering problems, block Krylov methods are an important tool for solution of large linear systems with multiple right hand sides. In addition to that, block methods reduce memory-access cost and increase efficient data reuse because they allow multiple matrixvector products with less memory access. However, their robustness problem and preconditioning are difficult to handle. So, to come up with a robust implementation of block Krylov methods, we initiated BIM++ (Block Iterative Methods) project, which is devoted to research and development of block Krylov methods to make them easier to use. BIM++ package is a high performance implementation of block Krylov methods written in C/C++ under GPL license, for solution of both symmetric and nonsymmetrical large linear systems with multiple right hand sides. In addition to this BIM++ includes important non-block Krylov methods such as CG (conjugate gradient), BICGSTAB (bi-conjugate gradient stabilized), GMRES (generalized minimal residual) and GMRES(m) (GMRES restarted). While developing BIM++, we stick to "keep-it-easy rule" and put performance first. Easy-to-use and easy-to-install are also important. While developing BIM++, our goals are 1) creating an environment for easy implementation and easy development of advanced numerical linear algebra algorithms, 2) creating a high performance and user friendly package, 3) enable to utilize C++ technologies, 4) enable to programming Krylov methods shorter and more readable, 5) enable to use block Krylov methods handy, 6) creating reusable, portable and easily upgradeable package, 7) enable to use BIM++ in Windows PCs, 8) creating a clear documentation and a webpage. To achieve these goals, we borrowed many good ideas from LAPACK++ and IML++.… [ABSTRACT FROM AUTHOR]