Context adaptivity for selected computational kernels with applications in optoelectronics and in phylogenetics

Computational Kernels sind der kritische Teil rechenintensiver Software, wofür der größte Rechenaufwand anfällt; daher müssen deren Design und Implementierung sorgfältig vorgenommen werden. Zwei wissenschaftliche Anwendungsprobleme aus der Optoelektronik und aus der Phylogenetik, sowie dazugehörige Computational Kernels motivieren diese Arbeit. Im ersten Anwendungsproblem werden Komponenten zur Berechnung komplex-symmetrischer Eigenwertprobleme diskutiert, welche in der Simulation von Wellenleitern in der Optoelektronik auftreten. LAPACK und ScaLAPACK beinhalten sehr leistungsfähige Referenzimplementierungen für bestimmte Problemstellungen der linearen Algebra. In Bezug auf Eigenwertprobleme werden ausschließlich reell-symmetrische und komplex-hermitesche Varianten angeboten, daher sind effiziente Codes für komplex-symmetrische (nicht-hermitesche) Eigenwertprobleme sehr wünschenswert. Das zweite Anwendungsproblem behandelt einen parallelen, wissenschaftlichen Workflow zur Rekonstruktion von Phylogenien, welcher entworfen, umgesetzt und evaluiert wird. Die Rekonstruktion von phylogenetischen Bäumen ist ein NP-hartes Problem, welches äußerst viel Rechenkapazität benötigt, wodurch ein paralleler Ansatz erforderlich ist. Die grundlegende Idee dieser Arbeit ist die Untersuchung der Wechselbeziehung zwischen dem Kontext der behandelten Kernels und deren Effizienz. Ein Kontext eines Computational Kernels beinhaltet Modellaspekte (z.B. Struktur der Eingabedaten), Softwareaspekte (z.B. rechenintensive Bibliotheken), Hardwareaspekte (z.B. verfügbarer Hauptspeicher und unterstützte darstellbare Genauigkeit), sowie weitere Anforderungen bzw. Einschränkungen. Einschränkungen sind hinsichtlich Laufzeit, Speicherverbrauch, gelieferte Genauigkeit usw., möglich. Das Konzept der Kontextadaptivität wird für ausgewählte Anwendungsprobleme in Computational Science gezeigt. Die vorgestellte Methode ist ein Meta-Algorithmus, der Aspekte des Kontexts verwendet, um optimale Leistung hinsichtlich der angewandten Metrik zu erzielen. Es ist wichtig, den Kontext einzubeziehen, weil Anforderungen gegeneinander ausgetauscht werden könnten, resultierend in einer höheren Leistung. Zum Beispiel kann im Falle einer niedrigen benötigten Genauigkeit ein schnellerer Algorithmus einer bewährten, aber langsameren, Methode vorgezogen werden. Speziell für komplex-symmetrische Eigenwertprobleme zugeschnittene Codes zielen darauf ab, Genauigkeit gegen Geschwindigkeit einzutauschen. Die Innovation wird durch neue algorithmische Ansätze belegt, welche die algebraische Struktur ausnutzen. Bezüglich der Berechnung von phylogenetischen Bäumen wird die Abbildung eines Workflows auf ein Campusgrid-System gezeigt. Die Innovation besteht in der anpassungsfähigen Implementierung des Workflows, der nebenläufige Instanzen von Computational Kernels in einem verteilten System darstellt. Die Adaptivität bezeichnet hier die Fähigkeit des Workflows, die Rechenlast hinsichtlich verfügbarer Rechner, Zeit und Qualität der phylogenetischen Bäume anzupassen. Kontextadaptivität wird durch die Implementierung und Evaluierung von wissenschaftlichen Problemstellungen aus der Optoelektronik und aus der Phylogenetik gezeigt. Für das Fachgebiet der Optoelektronik zielt eine Familie von Algorithmen auf die Lösung von verallgemeinerten komplex-symmetrischen Eigenwertproblemen ab. Unser alternativer Ansatz nutzt die symmetrische Struktur aus und spielt günstigere Laufzeit gegen eine geringere Genauigkeit aus. Dieser Ansatz ist somit schneller, jedoch (meist) ungenauer als der konventionelle Lösungsweg. Zusätzlich zum sequentiellen Löser wird eine parallele Variante diskutiert und teilweise auf einem Cluster mit bis zu 1024 CPU-Cores evaluiert. Die erzielten Laufzeiten beweisen die Überlegenheit unseres Ansatzes -- allerdings sind weitere Untersuchungen zur Erhöhung der Genauigkeit notwendig. Für das Fachgebiet der Phylogenetik zeigen wir, dass die phylogenetische Baum-Rekonstruktion mittels eines Condor-basierten Campusgrids effizient parallelisiert werden kann. Dieser parallele wissenschaftliche Workflow weist einen geringen parallelen Overhead auf, resultierend in exzellenter Effizienz.Computational kernels are the crucial part of computationally intensive software, where most of the computing time is spent; hence, their design and implementation have to be accomplished carefully. Two scientific application problems from optoelectronics and from phylogenetics and corresponding computational kernels are motivating this thesis. In the first application problem, components for the computational solution of complex symmetric EVPs are discussed, arising in the simulation of waveguides in optoelectronics. LAPACK and ScaLAPACK contain highly effective reference implementations for certain numerical problems in linear algebra. With respect to EVPs, only real symmetric and complex Hermitian codes are available, therefore efficient codes for complex symmetric (non-Hermitian) EVPs are highly desirable. In the second application problem, a parallel scientific workflow for computing phylogenies is designed, implemented, and evaluated. The reconstruction of phylogenetic trees is an NP-hard problem that demands huge scale computing capabilities, and therefore a parallel approach is necessary. One idea underlying this thesis is to investigate the interaction between the context of the kernels considered and their efficiency. The context of a computational kernel comprises model aspects (for instance, structure of input data), software aspects (for instance, computational libraries), hardware aspects (for instance, available RAM and supported precision), and certain requirements or constraints. Constraints may exist with respect to runtime, memory usage, accuracy required, etc.. The concept of context adaptivity is demonstrated to selected computational problems in computational science. The method proposed here is a meta-algorithm that utilizes aspects of the context to result in an optimal performance concerning the applied metric. It is important to consider the context, because requirements may be traded for each other, resulting in a higher performance. For instance, in case of a low required accuracy, a faster algorithmic approach may be favored over an established but slower method. With respect to EVPs, prototypical codes that are especially targeted at complex symmetric EVPs aim at trading accuracy for speed. The innovation is evidenced by the implementation of new algorithmic approaches exploiting structure. Concerning the computation of phylogenetic trees, the mapping of a scientific workflow onto a campus grid system is demonstrated. The adaptive implementation of the workflow features concurrent instances of a computational kernel on a distributed system. Here, adaptivity refers to the ability of the workflow to vary computational load in terms of available computing resources, available time, and quality of reconstructed phylogenetic trees. Context adaptivity is discussed by means of computational problems from optoelectronics and from phylogenetics. For the field of optoelectronics, a family of implemented algorithms aim at solving generalized complex symmetric EVPs. Our alternative approach exploiting structural symmetry trades runtime for accuracy, hence, it is faster but (usually) features a lower accuracy than the conventional approach. In addition to a complete sequential solver, a parallel variant is discussed and partly evaluated on a cluster utilizing up to 1024 CPU cores. Achieved runtimes evidence the superiority of our approach, however, further investigations on improving accuracy are suggested. For the field of phylogenetics, we show that phylogenetic tree reconstruction can efficiently be parallelized on a campus grid infrastructure. The parallel scientific workflow features a moderate parallel overhead, resulting in an excellent efficiency

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