Variational Theory and Domain Decomposition for Nonlocal Problems

In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish the well-posedness of associated boundary value problems, proving a nonlocal Poincar\'{e} inequality. To determine the conditioning of the discretized operator, we prove a spectral equivalence which leads to a mesh size independent upper bound for the condition number of the stiffness matrix. We then introduce a nonlocal two-domain variational formulation utilizing nonlocal transmission conditions, and prove equivalence with the single-domain formulation. A nonlocal Schur complement is introduced. We establish condition number bounds for the nonlocal stiffness and Schur complement matrices. Supporting numerical experiments demonstrating the conditioning of the nonlocal one- and two-domain problems are presented.Comment: Updated the technical part. In press in Applied Mathematics and Computatio

An odyssey into local refinement and multilevel preconditioning III: Implementation and numerical experiments

In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform refinement-based discretizations of elliptic equations, they tend to be less effective for algebraic systems, which arise from discretizations on locally refined meshes, losing their optimal behavior in both storage and computational complexity. Our primary focus here is on Bramble, Pasciak, and Xu (BPX)-style additive and multiplicative multilevel preconditioners, and on various stabilizations of the additive and multiplicative hierarchical basis (HB) method, and their use in the local mesh refinement setting. In parts I and II of this trilogy, it was shown that both BPX and wavelet stabilizations of HB have uniformly bounded condition numbers on several classes of locally refined two- and three-dimensional meshes based on fairly standard (and easily implementable) red and red-green mesh refinement algorithms. In this third part of the trilogy, we describe in detail the implementation of these types of algorithms, including detailed discussions of the data structures and traversal algorithms we employ for obtaining optimal storage and computational complexity in our implementations. We show how each of the algorithms can be implemented using standard data types, available in languages such as C and FORTRAN, so that the resulting algorithms have optimal (linear) storage requirements, and so that the resulting multilevel method or preconditioner can be applied with optimal (linear) computational costs. We have successfully used these data structure ideas for both MATLAB and C implementations using the FEtk, an open source finite element software package. We finish the paper with a sequence of numerical experiments illustrating the effectiveness of a number of BPX and stabilized HB variants for several examples requiring local refinement

Multilevel Solvers for Unstructured Surface Meshes

Parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner

Ülke riskinin göstergesi olarak kredi temerrüt swaplarını etkileyen faktörler : asimetrik nedensellik yöntemi

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Kredi türevleri kredi riskinden korunmak amacıyla başvurulan türev enstrümanlardır. Kredi temerrüt swapları ise kredi türevleri arasında en çok tercih edilen kontratlar olarak karşımıza çıkmaktadır. Çalışmada çoğunlukla CDS (Credit Default Swap) olarak anılan kredi temerrüt swapları, kısaca temerrüt riskine karşı yapılan bir sigorta sözleşmesi olarak düşünülebilir. CDS sözleşmeleri alıcısına belli aralıklarla ödenen primler karşılığında temerrüt riskinden korunma imkanı sağlamaktadır. CDS'lerin dayanak varlıklarını tahvil, kredi gibi borç yükümlülükleri oluşturmaktadır. Bu borç yükümlülükleri şirketlere, finansal kuruluşlara veya ülkelere ait olabilmektedir. Temerrüt riskinden korunmak amacıyla çıkarılan bu sözleşmelerin diğer işlevi ise temerrüt riskini yansıtmalarıdır. CDS'ler özellikle son yıllarda ülke temerrüt riskinin önemli bir göstergesi olarak sıklıkla başvurulan bir araç haline gelmiştir. Çalışmamızda ülke riskinin göstergesi olarak ele alınan CDS'ler ve ülke CDS primlerini etkilediği düşünülen finansal değişkenler arasındaki nedensellik ilişkisi incelenmektedir. Bu amaçla çalışmada; Türkiye, Japonya, Çin, Brezilya, Arjantin, Meksika, Endonezya, Filipinler, Rusya, Güney Kore, Polonya, Malezya, Almanya, Portekiz, İtalya, İspanya ve Fransa'dan oluşan 17 ülkeye ait 2005-2015 arasındaki CDS primleri ile Amerikan doları döviz kuru, Amerika 10 yıl vadeli devlet tahvili faiz oranı ve VIX endeksi arasındaki nedensellik ilişkisi araştırılmaktadır. Çalışmada bu ilişkiyi ortaya koymak için simetrik ve asimetrik olmak üzere iki test uygulanmıştır. Bu testlerden ilki Granger nedensellik testi, diğeri de Hatemi-J (2012) asimetrik nedensellik testidir. Çalışmanın sonucunda CDS primleri ile seçilen finansal değişkenler arasında asimetrik nedensellik ilişkisi olduğu görülmüştür. Ayrıca, Hatemi-J asimetrik nedensellik testinin CDS primleri ve seçilen finansal değişkenler arasındaki nedensellik ilişkisini açıklamakta Granger testine göre daha etkili olduğu gözlemlenmiştir. Anahtar Kelimeler: Kredi Temerrüt Swapları, Ülke Riski, Kredi Türevleri, Asimetrik Nedensellik Testi, Granger Nedensellik TestiCredit derivatives are derivative instruments that are used to hedge against credit risk. Credit default swaps are the most preferred contracts among credit derivatives. Credit default swaps, often referred to as CDS (Credit Default Swap) in this study, can be considered as an insurance contract against the default risk. CDS contracts provide protection for the buyer against default risk in return for certain premiums. The underlying assets of CDSs are debt obligations such as bonds and loans. These debt obligations may belong to companies, financial institutions or countries. The other function of these contracts issued to protect against default risk is to reflect default risk. CDS has become a frequent tool in recent years as an important indicator of sovereign default risk. In this study, we examine the causality relationship between the CDS's which are considered as an indicative of the country's risk and the financial variables that are thought to affect the country's CDS premiums. For this purpose; the casuality relationship between CDS premiums for 2005-2015 belonging to 17 countries, including Turkey, Japan, China, Brazil, Argentina, Mexico, Indonesia, Philippines, Russia, South Korea, Poland, Malaysia, Germany, Portugal, Italy, Spain and France, and US dollar currency, US 10-year government bond interest rate and VIX index is investigated. Two tests, symmetric and asymmetric, were applied to reveal this relationship in the study. First test is the Granger causality test and the second test is Hatemi-J (2012) asymmetric causality test. As a result of the study, it is seen that there is an asymmetric causality relationship between CDS premiums and selected financial variables. It is also observed that Hatemi-J asymmetric causality test is more effective than the Granger test in explaining the causality relationship between CDS premiums and selected financial variables. Keywords: Credit Default Swaps, Sovereign Risk, Credit Derivatives,Asymmetric Casuality Test, Granger Casuality Tes

The effect of impregnation strategy on methane dry reforming activity of Ce promoted Pt/ZrO2

Cataloged from PDF version of article.Dry reforming of methane has been studied over Pt/ZrO2 catalysts promoted with Ce for different temperatures and feed compositions. The influence of the impregnation strategy and the cerium amount on the activity and stability of the catalysts were investigated. The results have shown that introduction of 1 wt.% Ce to the Pt/ZrO2 catalyst via coimpregnation method led to the highest catalytic activity and stability. 1 wt.%Ce-1 wt.%Pt/ZrO2 catalyst prepared by sequential impregnation displayed inferior CH4 and CO2 conversion performances with lowest H-2/CO production ratios. 1 wt.%Ce-1 wt.%Pt/ZrO2 catalyst prepared by coimpregnation showed the highest activity even for the feed with high CH4/CO2 ratio. The reason for high activity was explained by the intensive interaction between Pt and Ce phases for coimpregnated sample, which had been verified by X-ray photoelectron spectroscopy and Energy Dispersive X-Ray analyses. Strong and extensive Pt-Ce surface interaction results in an increase in the number of Ce3+ sites and enhances the dispersion of Pt. (C) 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved