Algorithms for massively parallel generic hp-adaptive finite element methods

Efficient algorithms for the numerical solution of partial differential equations are required to solve problems on an economically viable timescale. In general, this is achieved by adapting the resolution of the discretization to the investigated problem, as well as exploiting hardware specifications. For the latter category, parallelization plays a major role for modern multi-core and multi-node architectures, especially in the context of high-performance computing. Using finite element methods, solutions are approximated by discretizing the function space of the problem with piecewise polynomials. With hp-adaptive methods, the polynomial degrees of these basis functions may vary on locally refined meshes. We present algorithms and data structures required for generic hp-adaptive finite element software applicable for both continuous and discontinuous Galerkin methods on distributed memory systems. Both function space and mesh may be adapted dynamically during the solution process. We cover details concerning the unique enumeration of degrees of freedom with continuous Galerkin methods, the communication of variable size data, and load balancing. Furthermore, we present strategies to determine the type of adaptation based on error estimation and prediction as well as smoothness estimation via the decay rate of coefficients of Fourier and Legendre series expansions. Both refinement and coarsening are considered. A reference implementation in the open-source library deal.II is provided and applied to the Laplace problem on a domain with a reentrant corner which invokes a singularity. With this example, we demonstrate the benefits of the hp-adaptive methods in terms of error convergence and show that our algorithm scales up to 49,152 MPI processes.Für die numerische Lösung partieller Differentialgleichungen sind effiziente Algorithmen erforderlich, um Probleme auf einer wirtschaftlich tragbaren Zeitskala zu lösen. Im Allgemeinen ist dies durch die Anpassung der Diskretisierungsauflösung an das untersuchte Problem sowie durch die Ausnutzung der Hardwarespezifikationen möglich. Für die letztere Kategorie spielt die Parallelisierung eine große Rolle für moderne Mehrkern- und Mehrknotenarchitekturen, insbesondere im Kontext des Hochleistungsrechnens. Mit Hilfe von Finite-Elemente-Methoden werden Lösungen durch Diskretisierung des assoziierten Funktionsraums mit stückweisen Polynomen approximiert. Bei hp-adaptiven Verfahren können die Polynomgrade dieser Basisfunktionen auf lokal verfeinerten Gittern variieren. In dieser Dissertation werden Algorithmen und Datenstrukturen vorgestellt, die für generische hp-adaptive Finite-Elemente-Software benötigt werden und sowohl für kontinuierliche als auch diskontinuierliche Galerkin-Verfahren auf Systemen mit verteiltem Speicher anwendbar sind. Sowohl der Funktionsraum als auch das Gitter können während des Lösungsprozesses dynamisch angepasst werden. Im Besonderen erläutert werden die eindeutige Nummerierung von Freiheitsgraden mit kontinuierlichen Galerkin-Verfahren, die Kommunikation von Daten variabler Größe und die Lastenverteilung. Außerdem werden Strategien zur Bestimmung des Adaptierungstyps auf der Grundlage von Fehlerschätzungen und -prognosen sowie Glattheitsschätzungen vorgestellt, die über die Zerfallsrate von Koeffizienten aus Reihenentwicklungen nach Fourier und Legendre bestimmt werden. Dabei werden sowohl Verfeinerung als auch Vergröberung berücksichtigt. Eine Referenzimplementierung erfolgt in der Open-Source-Bibliothek deal.II und wird auf das Laplace-Problem auf einem Gebiet mit einer einschneidenden Ecke angewandt, die eine Singularität aufweist. Anhand dieses Beispiels werden die Vorteile der hp-adaptiven Methoden hinsichtlich der Fehlerkonvergenz und die Skalierbarkeit der präsentierten Algorithmen auf bis zu 49.152 MPI-Prozessen demonstriert

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis

Differential cross section measurements for the production of a W boson in association with jets in proton–proton collisions at √s = 7 TeV

Measurements are reported of differential cross sections for the production of a W boson, which decays into a muon and a neutrino, in association with jets, as a function of several variables, including the transverse momenta (pT) and pseudorapidities of the four leading jets, the scalar sum of jet transverse momenta (HT), and the difference in azimuthal angle between the directions of each jet and the muon. The data sample of pp collisions at a centre-of-mass energy of 7 TeV was collected with the CMS detector at the LHC and corresponds to an integrated luminosity of 5.0 fb[superscript −1]. The measured cross sections are compared to predictions from Monte Carlo generators, MadGraph + pythia and sherpa, and to next-to-leading-order calculations from BlackHat + sherpa. The differential cross sections are found to be in agreement with the predictions, apart from the pT distributions of the leading jets at high pT values, the distributions of the HT at high-HT and low jet multiplicity, and the distribution of the difference in azimuthal angle between the leading jet and the muon at low values.United States. Dept. of EnergyNational Science Foundation (U.S.)Alfred P. Sloan Foundatio

Search for stop and higgsino production using diphoton Higgs boson decays

Results are presented of a search for a "natural" supersymmetry scenario with gauge mediated symmetry breaking. It is assumed that only the supersymmetric partners of the top-quark (stop) and the Higgs boson (higgsino) are accessible. Events are examined in which there are two photons forming a Higgs boson candidate, and at least two b-quark jets. In 19.7 inverse femtobarns of proton-proton collision data at sqrt(s) = 8 TeV, recorded in the CMS experiment, no evidence of a signal is found and lower limits at the 95% confidence level are set, excluding the stop mass below 360 to 410 GeV, depending on the higgsino mass

Impacts of the Tropical Pacific/Indian Oceans on the Seasonal Cycle of the West African Monsoon

The current consensus is that drought has developed in the Sahel during the second half of the twentieth century as a result of remote effects of oceanic anomalies amplified by local land–atmosphere interactions. This paper focuses on the impacts of oceanic anomalies upon West African climate and specifically aims to identify those from SST anomalies in the Pacific/Indian Oceans during spring and summer seasons, when they were significant. Idealized sensitivity experiments are performed with four atmospheric general circulation models (AGCMs). The prescribed SST patterns used in the AGCMs are based on the leading mode of covariability between SST anomalies over the Pacific/Indian Oceans and summer rainfall over West Africa. The results show that such oceanic anomalies in the Pacific/Indian Ocean lead to a northward shift of an anomalous dry belt from the Gulf of Guinea to the Sahel as the season advances. In the Sahel, the magnitude of rainfall anomalies is comparable to that obtained by other authors using SST anomalies confined to the proximity of the Atlantic Ocean. The mechanism connecting the Pacific/Indian SST anomalies with West African rainfall has a strong seasonal cycle. In spring (May and June), anomalous subsidence develops over both the Maritime Continent and the equatorial Atlantic in response to the enhanced equatorial heating. Precipitation increases over continental West Africa in association with stronger zonal convergence of moisture. In addition, precipitation decreases over the Gulf of Guinea. During the monsoon peak (July and August), the SST anomalies move westward over the equatorial Pacific and the two regions where subsidence occurred earlier in the seasons merge over West Africa. The monsoon weakens and rainfall decreases over the Sahel, especially in August.Peer reviewe

Severe early onset preeclampsia: short and long term clinical, psychosocial and biochemical aspects

Preeclampsia is a pregnancy specific disorder commonly defined as de novo hypertension and proteinuria after 20 weeks gestational age. It occurs in approximately 3-5% of pregnancies and it is still a major cause of both foetal and maternal morbidity and mortality worldwide1. As extensive research has not yet elucidated the aetiology of preeclampsia, there are no rational preventive or therapeutic interventions available. The only rational treatment is delivery, which benefits the mother but is not in the interest of the foetus, if remote from term. Early onset preeclampsia (<32 weeks’ gestational age) occurs in less than 1% of pregnancies. It is, however often associated with maternal morbidity as the risk of progression to severe maternal disease is inversely related with gestational age at onset2. Resulting prematurity is therefore the main cause of neonatal mortality and morbidity in patients with severe preeclampsia3. Although the discussion is ongoing, perinatal survival is suggested to be increased in patients with preterm preeclampsia by expectant, non-interventional management. This temporising treatment option to lengthen pregnancy includes the use of antihypertensive medication to control hypertension, magnesium sulphate to prevent eclampsia and corticosteroids to enhance foetal lung maturity4. With optimal maternal haemodynamic status and reassuring foetal condition this results on average in an extension of 2 weeks. Prolongation of these pregnancies is a great challenge for clinicians to balance between potential maternal risks on one the eve hand and possible foetal benefits on the other. Clinical controversies regarding prolongation of preterm preeclamptic pregnancies still exist – also taking into account that preeclampsia is the leading cause of maternal mortality in the Netherlands5 - a debate which is even more pronounced in very preterm pregnancies with questionable foetal viability6-9. Do maternal risks of prolongation of these very early pregnancies outweigh the chances of neonatal survival? Counselling of women with very early onset preeclampsia not only comprises of knowledge of the outcome of those particular pregnancies, but also knowledge of outcomes of future pregnancies of these women is of major clinical importance. This thesis opens with a review of the literature on identifiable risk factors of preeclampsia

Search for heavy resonances decaying to two Higgs bosons in final states containing four b quarks

A search is presented for narrow heavy resonances X decaying into pairs of Higgs bosons (H) in proton-proton collisions collected by the CMS experiment at the LHC at root s = 8 TeV. The data correspond to an integrated luminosity of 19.7 fb(-1). The search considers HH resonances with masses between 1 and 3 TeV, having final states of two b quark pairs. Each Higgs boson is produced with large momentum, and the hadronization products of the pair of b quarks can usually be reconstructed as single large jets. The background from multijet and t (t) over bar events is significantly reduced by applying requirements related to the flavor of the jet, its mass, and its substructure. The signal would be identified as a peak on top of the dijet invariant mass spectrum of the remaining background events. No evidence is observed for such a signal. Upper limits obtained at 95 confidence level for the product of the production cross section and branching fraction sigma(gg -> X) B(X -> HH -> b (b) over barb (b) over bar) range from 10 to 1.5 fb for the mass of X from 1.15 to 2.0 TeV, significantly extending previous searches. For a warped extra dimension theory with amass scale Lambda(R) = 1 TeV, the data exclude radion scalar masses between 1.15 and 1.55 TeV

Search for supersymmetry in events with one lepton and multiple jets in proton-proton collisions at root s=13 TeV

Peer reviewe