In Memory of Vladimir Gerdt

Center for Computational Methods in Applied Mathematics of RUDN, Professor V.P. Gerdt, whose passing was a great loss to the scientific center and the computer algebra community. The article provides biographical information about V.P. Gerdt, talks about his contribution to the development of computer algebra in Russia and the world. At the end there are the author’s personal memories of V.P. Gerdt.Настоящая статья - мемориальная, она посвящена памяти руководителя научного центра вычислительных методов в прикладной математике РУДН, профессора В.П. Гердта, чей уход стал невосполнимой потерей для научного центра и всего сообщества компьютерной алгебры. В статье приведены биографические сведения о В.П. Гердте, рассказано о его вкладе в развитие компьютерной алгебры в России и мире. В конце приведены личные воспоминания автора о В.П. Гердте

Algebraic Construction of a Strongly Consistent, Permutationally Symmetric and Conservative Difference Scheme for 3D Steady Stokes Flow

By using symbolic algebraic computation, we construct a strongly-consistent second-order finite difference scheme for steady three-dimensional Stokes flow and a Cartesian solution grid. The scheme has the second order of accuracy and incorporates the pressure Poisson equation. This equation is the integrability condition for the discrete momentum and continuity equations. Our algebraic approach to the construction of difference schemes suggested by the second and the third authors combines the finite volume method, numerical integration, and difference elimination. We make use of the techniques of the differential and difference Janet/Gröbner bases for performing related computations. To prove the strong consistency of the generated scheme, we use these bases to correlate the differential ideal generated by the polynomials in the Stokes equations with the difference ideal generated by the polynomials in the constructed difference scheme. As this takes place, our difference scheme is conservative and inherits permutation symmetry of the differential Stokes flow. For the obtained scheme, we compute the modified differential system and use it to analyze the scheme’s accuracy

Algebraic Construction of a Strongly Consistent, Permutationally Symmetric and Conservative Difference Scheme for 3D Steady Stokes Flow

By using symbolic algebraic computation, we construct a strongly-consistent second-order finite difference scheme for steady three-dimensional Stokes flow and a Cartesian solution grid. The scheme has the second order of accuracy and incorporates the pressure Poisson equation. This equation is the integrability condition for the discrete momentum and continuity equations. Our algebraic approach to the construction of difference schemes suggested by the second and the third authors combines the finite volume method, numerical integration, and difference elimination. We make use of the techniques of the differential and difference Janet/Grobner bases for performing related computations. To prove the strong consistency of the generated scheme, we use these bases to correlate the differential ideal generated by the polynomials in the Stokes equations with the difference ideal generated by the polynomials in the constructed difference scheme. As this takes place, our difference scheme is conservative and inherits permutation symmetry of the differential Stokes flow. For the obtained scheme, we compute the modified differential system and use it to analyze the scheme's accuracy

Globally Optimal Catalysts: Computerbasierte Optimierung von abstrakten katalytischen Einbettungen für beliebige chemische Reaktionen

In the context of inverse design of molecules with desired optimal properties, the long-term goal of this Thesis is to develop a general framework which tackles the design of molecular systems for an optimal catalytic effect onto arbitrary chemical reactions. For any given reaction, an arrangement of an additional molecular framework around this reaction center is sought such that the energetic reaction barrier is lowered as much as possible. As necessary abstraction layer, the so-called globally optimal catalyst (GOCAT) model is introduced, and, furthermore, evolutionary algorithms (EAs) are harnessed as implemented in our global optimization suite for chemical problems, ogolem, which was highly extended to allow for these catalysis optimizations. Starting with a maximally reductionistic approach for studying the non-bonding interactions, electrostatic GOCATs are introduced that consist of arbitrary numbers, distributions and strengths of partial point charges around reacting molecules, mostly surrounding these on a common exposed surface. In the end, two reactions are studied in detail within the general topic of electrostatic catalysis. Some of the initially present model approximations are already sufficiently lifted, still-existing ones are critically assessed and further future extensions to the framework are discussed. Moreover, many method development matters are addressed: They range from optimal shared-memory parallelization, exemplified for global parameter optimization of the reactive force field, ReaxFF, via diversity control parameters for the EAs, applied to a cluster structure optimization problem, to EA operator benchmarks and optimizations of abstract electrostatics.Im Kontext von inversem Design von Molekülen mit optimalen Eigenschaften versucht die vorliegende Arbeit als Langzeitziel eine passende Plattform zu entwickeln, welche das generelle Design molekularer Systeme für einen optimalen Katalyseeffekt auf beliebige chemische Reaktionen projektiert. Für eine gegeben Reaktion soll eine hinzukommende chemische Umgebung komponiert werden, welche die Reaktionsenergiebarriere so weit wie möglich vermindert. Als notwendige Abstraktionsschicht wird das sogenannte Modell des globally optimal catalyst (GOCAT) eingeführt und außerdem kommen Evolutionäre Algorithmen (EAs) zur Anwendung, wie sie bereits in unserem Programmpaket zur Lösung allgemeiner globaler Optimierungsprobleme der Chemie, ogolem, bereitgestellt werden, welches jedoch deutlich für diese Katalyseoptimierungen ergänzt wurde. Angefangen in einem maximal-reduktionistischen Ansatz werden elektrostatische GOCATs erarbeitet, die aus einer beliebigen Anzahl, Verteilung und Stärke von Partialladungen bestehen und rund um die reagierenden Moleküle drapiert werden, meist auf einer gemeinsamen exponierten Oberfläche. Insgesamt werden zwei Reaktionen detailliert untersucht im generellen Kontext von elektrostatischer Katalyse. Einige eingangs vorhandene Modellannahmen werden bereits systematisch verbessert, noch vorhandene kritisch beleuchtet und künftige Erweiterungen auseinandergesetzt. Weiterhin werden unterschiedliche Methodenentwicklungsaspekte angesprochen: Diese reichen von verbesserter Parallelisierung in Mehrprozessorarchitekturen, beispielhaft gezeigt anhand einer globalen Parameteroptimierung des reaktiven Kraftfeldes ReaxFF, über Diversitätskontrollparameter des EAs, illustriert mittels eines Clusterstrukturoptimierungsproblems, bis hin zu EA-Operator-Testevaluationen und allgemeinen abstrakten Elektrostatikoptimierungen