Implementation of a parallel algorithm for the symmetric positive definite systems of equations on the CRAY-T3E

A parallel algorithm for the solution of dense Symmetric Positive Definite (SPD) systems of equations Ax = b has been designed for the implementation on the CRAY T3E. One of the numerically stable methods for the solution of this system is proposed by Delosme & Ipsen [3]. In order to implement this algorithm on the CRAY T3E, we require to handle the procedures involved in a slightly different way. These implementation issues are discussed in detail. The actual timings for different communication schemes, on different sets of data values and varying number of processors have been tested and reported

Parameter Identification in a Tuberculosis Model for Cameroon

A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as both frequency-and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years.IMU Berlin Einstein Foundation Progra

Model-based exploration of hypokalemia in dairy cows

Hypokalemia in dairy cows, which is characterized by too low serum potassium levels, is a severe mineral disorder that can be life threatening. In this paper, we explore different originating conditions of hypokalemia—reduced potassium intake, increased excretion, acid-base disturbances, and increased insulin—by using a dynamic mathematical model for potassium balance in non-lactating and lactating cows. The simulations confirm observations described in literature. They illustrate, for example, that changes in dietary intake or excretion highly effect intracellular potassium levels, whereas extracellular levels vary only slightly. Simulations also show that the higher the potassium content in the diet, the more potassium is excreted with urine. Application of the mathematical model assists in experimental planning and therefore contributes to the 3R strategy: reduction, refinement and replacement of animal experiments

Model-based exploration of hypokalemia in dairy cows

Hypokalemia in dairy cows, which is characterized by too low serum potassium levels, is a severe mineral disorder that can be life threatening. In this paper, we explore different originating conditions of hypokalemia—reduced potassium intake, increased excretion, acid-base disturbances, and increased insulin—by using a dynamic mathematical model for potassium balance in non-lactating and lactating cows. The simulations confirm observations described in literature. They illustrate, for example, that changes in dietary intake or excretion highly effect intracellular potassium levels, whereas extracellular levels vary only slightly. Simulations also show that the higher the potassium content in the diet, the more potassium is excreted with urine. Application of the mathematical model assists in experimental planning and therefore contributes to the 3R strategy: reduction, refinement and replacement of animal experiments.publishedVersio

Quantifying Asymmetry in Gait: The Weighted Universal Symmetry Index to Evaluate 3D Ground Reaction Forces

Though gait asymmetry is used as a metric of functional recovery in clinical rehabilitation, there is no consensus on an ideal method for its evaluation. Various methods have been proposed to analyze single bilateral signals but are limited in scope, as they can often use only positive signals or discrete values extracted from time-scale data as input. By defining five symmetry axioms, a framework for benchmarking existing methods was established and a new method was described here for the first time: the weighted universal symmetry index (wUSI), which overcomes limitations of other methods. Both existing methods and the wUSI were mathematically compared to each other and in respect to their ability to fulfill the proposed symmetry axioms. Eligible methods that fulfilled these axioms were then applied using both discrete and continuous approaches to ground reaction force (GRF) data collected from healthy gait, both with and without artificially induced asymmetry using a single instrumented elbow crutch. The wUSI with a continuous approach was the only symmetry method capable of identifying GRF asymmetry differences in different walking conditions in all three planes of motion. When used with a continuous approach, the wUSI method was able to detect asymmetries while avoiding artificial inflation, a common problem reported in other methods. In conclusion, the wUSI is proposed as a universal method to quantify three-dimensional GRF asymmetries, which may also be expanded to other biomechanical signals

Macroscale mesenchymal condensation to study cytokine-driven cellular and matrix-related changes during cartilage degradation

Understanding the pathophysiological processes of cartilage degradation requires adequate model systems to develop therapeutic strategies towards osteoarthritis (OA). Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific disease aspects. This study aimed to combine in vitro and in silico modeling based on a tissue-engineering approach using mesenchymal condensation to mimic cytokine-induced cellular and matrix-related changes during cartilage degradation. Thus, scaffold-free cartilage-like constructs (SFCCs) were produced based on self-organization of mesenchymal stromal cells (mesenchymal condensation) and (i) characterized regarding their cellular and matrix composition or secondly (ii) treated with interleukin-1β (IL–1β) and tumor necrosis factor α (TNFα) for 3 weeks to simulate OA-related matrix degradation. In addition, an existing mathematical model based on partial differential equations was optimized and transferred to the underlying settings to simulate the distribution of IL–1β, type II collagen degradation and cell number reduction. By combining in vitro and in silico methods, we aimed to develop a valid, efficient alternative approach to examine and predict disease progression and effects of new therapeutics.publishedVersio

GMERR - an Error Minimizing Variant of GMRES

The paper analyzes a recently proposed iterative error minimizing method for the solution of linear systems. Sufficient and necessary conditions for convergence are studied, which show that the method essentially requires normal matrices. An efficient implementation similar to GMRES has been worked out in detail. Numerical tests on general non--normal matrices, of course, indicate that this approach is not competitive with GMRES. Summarizing, if error minimizing is important, one should rather choose CGNE. A computational niche for GMERR might be problems, where normal but non--symmetric matrices occur, like dissipative quantum mechanics. AMS Subject Classification: 65F10, 65F25, 65F50 Keywords: linear systems, Krylov subspace methods, error minimizing methods, preconditioning Contents 1 Introduction 1 2 Derivation of the method 1 3 Convergence analysis of GMERR 3 4 Algorithmic realization 8 5 Convergence control of GMERR 10 6 Numerical tests 11 References 13 Appendix 1: Iterative..

Massively Parallel Linearly-Implicit Extrapolation Algorithms as a Powerful Tool in Process Simulation

We study the parallelization of linearly--implicit extrapolation codes for the solution of large scale PDE systems and differential algebraic equations on distributed memory machines. The main advantage of these algorithms is that they enable adapativity both in time and space. Additive Krylov--Schwarz methods yield high parallel perfomance for such extrapolation methods. Our approach combines a slightly overlapping domain decomposition together with a polynomial block Neumann preconditioner and a reduced system technique. Furthermore we get important advantages through the explicit computation of the matrix--products of the preconditioner and the matrix of the linear system. The parallel algorithms exhibit scalability up to 64 processors already for medium--sized test problems. We show that the codes are really efficient in large application systems for chemical engineering problems

Parallel Extrapolation Methods and Their Application in Chemical Engineering

We study the parallelization of linearly--implicit extrapolation methods for the solution of large scale systems of differential algebraic equations arising in a method of lines (MOL) treatment of partial differential equations. In our approach we combine a slightly overlapping domain decomposition together with a polynomial block Neumann preconditioner. Through the explicit computation of the matrix products of the preconditioner and the system matrix a significant gain in overall efficiency is achieved for medium--sized problems. The parallel algorithm exhibits a good scalability up to 32 processors on a Cray T3E. Preliminary results for computations on a workstation cluster are reported