Numerical conservative solutions of the Hunter--Saxton equation

In the article a convergent numerical method for conservative solutions of the Hunter--Saxton equation is derived. The method is based on piecewise linear projections, followed by evolution along characteristics where the time step is chosen in order to prevent wave breaking. Convergence is obtained when the time step is proportional to the square root of the spatial step size, which is a milder restriction than the common CFL condition for conservation laws

Hyperbolic Techniques in Modelling, Analysis and Numerics

Several research areas are flourishing on the roots of the breakthroughs in conservation laws that took place in the last two decades. The meeting played a key role in providing contacts among the different branches that are currently developing. All the invitees shared the same common background that consists of the analytical and numerical techniques for nonlinear hyperbolic balance laws. However, their fields of applications and their levels of abstraction are very diverse. The workshop was the unique opportunity to share ideas about analytical issues like the fine-structure of singular solutions or the validity of entropy solution concepts. It turned out that generalized hyperbolic techniques are able to handle the challenges posed by new applications. The design of efficient structure preserving methods turned out to be the major line of development in numerical analysis

エネルギー関数を持つ発展方程式に対する幾何学的数値計算法

学位の種別: 課程博士審査委員会委員 : (主査)東京大学教授 松尾 宇泰, 東京大学教授 中島 研吾, 東京大学准教授 鈴木 秀幸, 東京大学准教授 長尾 大道, 東京大学准教授 齋藤 宣一University of Tokyo(東京大学

Bilinear Immersed Finite Elements for Interface Problems

In this dissertation we discuss bilinear immersed finite elements (IFE) for solving interface problems. The related research works can be categorized into three aspects: (1) the construction of the bilinear immersed finite element spaces; (2) numerical methods based on these IFE spaces for solving interface problems; and (3) the corresponding error analysis. All of these together form a solid foundation for the bilinear IFEs. The research on immersed finite elements is motivated by many real world applications, in which a simulation domain is often formed by several materials separated from each other by curves or surfaces while a mesh independent of interface instead of a body-fitting mesh is preferred. The bilinear IFE spaces are nonconforming finite element spaces and the mesh can be independent of interface. The error estimates for the interpolation of a Sobolev function in a bilinear IFE space indicate that this space has the usual approximation capability expected from bilinear polynomials, which is O(h2) in L2 norm and O(h) in H1 norm. Then the immersed spaces are applied in Galerkin, finite volume element (FVE) and discontinuous Galerkin (DG) methods for solving interface problems. Numerical examples show that these methods based on the bilinear IFE spaces have the same optimal convergence rates as those based on the standard bilinear finite element for solutions with certain smoothness. For the symmetric selective immersed discontinuous Galerkin method based on bilinear IFE, we have established its optimal convergence rate. For the Galerkin method based on bilinear IFE, we have also established its convergence. One of the important advantages of the discontinuous Galerkin method is its flexibility for both p and h mesh refinement. Because IFEs can use a mesh independent of interface, such as a structured mesh, the combination of a DG method and IFEs allows a flexible adaptive mesh independent of interface to be used for solving interface problems. That is, a mesh independent of interface can be refined wherever needed, such as around the interface and the singular source. We also develop an efficient selective immersed discontinuous Galerkin method. It uses the sophisticated discontinuous Galerkin formulation only around the locations needed, but uses the simpler Galerkin formulation everywhere else. This selective formulation leads to an algebraic system with far less unknowns than the immersed DG method without scarifying the accuracy; hence it is far more efficient than the conventional discontinuous Galerkin formulations

ECOS 2012

The 8-volume set contains the Proceedings of the 25th ECOS 2012 International Conference, Perugia, Italy, June 26th to June 29th, 2012. ECOS is an acronym for Efficiency, Cost, Optimization and Simulation (of energy conversion systems and processes), summarizing the topics covered in ECOS: Thermodynamics, Heat and Mass Transfer, Exergy and Second Law Analysis, Process Integration and Heat Exchanger Networks, Fluid Dynamics and Power Plant Components, Fuel Cells, Simulation of Energy Conversion Systems, Renewable Energies, Thermo-Economic Analysis and Optimisation, Combustion, Chemical Reactors, Carbon Capture and Sequestration, Building/Urban/Complex Energy Systems, Water Desalination and Use of Water Resources, Energy Systems- Environmental and Sustainability Issues, System Operation/ Control/Diagnosis and Prognosis, Industrial Ecology

Abstracts on Radio Direction Finding (1899 - 1995)

The files on this record represent the various databases that originally composed the CD-ROM issue of "Abstracts on Radio Direction Finding" database, which is now part of the Dudley Knox Library's Abstracts and Selected Full Text Documents on Radio Direction Finding (1899 - 1995) Collection. (See Calhoun record https://calhoun.nps.edu/handle/10945/57364 for further information on this collection and the bibliography). Due to issues of technological obsolescence preventing current and future audiences from accessing the bibliography, DKL exported and converted into the three files on this record the various databases contained in the CD-ROM. The contents of these files are: 1) RDFA_CompleteBibliography_xls.zip [RDFA_CompleteBibliography.xls: Metadata for the complete bibliography, in Excel 97-2003 Workbook format; RDFA_Glossary.xls: Glossary of terms, in Excel 97-2003 Workbookformat; RDFA_Biographies.xls: Biographies of leading figures, in Excel 97-2003 Workbook format]; 2) RDFA_CompleteBibliography_csv.zip [RDFA_CompleteBibliography.TXT: Metadata for the complete bibliography, in CSV format; RDFA_Glossary.TXT: Glossary of terms, in CSV format; RDFA_Biographies.TXT: Biographies of leading figures, in CSV format]; 3) RDFA_CompleteBibliography.pdf: A human readable display of the bibliographic data, as a means of double-checking any possible deviations due to conversion