High Performance Computing in Science and Engineering ’98

In particular in mathematics and natural sciences, the use of supercomputers has made possible the treatment of formerly completely intractable problems. It also provides the possibility of analyzing complex systems by the aid of simulation. This procedure is now becoming as important as theoretical investigations and closely interacts with the latter. A visionary formulation of the scientific potential arising from an optimal use of the supercomputers at the HLRS can be found in the “Report of the High Performance Computing and Networking (HPCN) Advisory Committee” already published in 1992:

A new link between Quantum Chromodynamics (QCD), the theory of strongly interacting elementary particles and mesoscopic systems in condensed matter physics is established through random matrix methods. Ensembles of complete eigenvalue spectra of the QCD Dirac operator are calculated for the first time for different lattice volumes ranging from lattice size 44 to 164. This amounts among other things to diagonalize sparse hermitean matrices of size 40 000 times 40 000 with very high precision for typical several thousand different matrices. The computation is only feasible on a massive paralell processing system like the CRAY T3E The remarkable agreement with the predictions of chiral random matrix models establishes the notion of universal fluctuations in systems with disorder and offers new insights into fundamental questions like spontaneous chiral symmetry breaking and the quark mass puzzle.

The geodynamo, i.e. the process by which the Earth’s magnetic field is generated in the liquid outer core of the Earth, is generally regarded as one of the fundamental problems of geophysics. It is the prevailing opinion among geophysicists that thermal and chemical buoyancy originating in connection with the solidification of the inner core and the general cooling of the Earth cause convection flows in the outer core which consists of liquid iron together with some lighter elements. The mechanical energy of the convection flow provides the energy for the sustenance of the magnetic field against Ohmic losses. The mechanism by which this transfer of energy is accomplished is called a homogeneous dynamo in order to distinguish it from the common inhomogeneous dynamos used in technical applications.

This article summarizes the results of a series of Monte Carlo simulations of persistent spins or “survivors” in the triangular Q-state Potts model. It is shown that the fraction F(t) of survivors decays algebraically in time t, with nontrivial exponents θ depending on Q but not on temperature T. At zero temperature, asymptotic exponents θ have been calculated for the whole range of Q = 3 to ∞. In accordance with exact results in one dimension and early Monte Carlo studies in two dimensions, θ increases from 0.31 to unity as Q increases from 3 to ∞. For small Q, it has also been shown that θ approaches the same universal value for both zero and non-zero temperatures (below the critical temperature Tc).

We show that quantum localization occurs in the center-of-mass motion of a two-level ion stored in a Paul trap and interacting with a standing laser field. The variable showing localization is identified to be the vibrational quantum number of a reference Floquet oscillator. The quantum localization length is shown to oscillate as a function of the atom-field detuning with a period given by the secular frequency of the trap. Furthermore, we simulate the effect of spontaneous emission on the system and show that in the limit of far detuning the phenomenon of dynamical localization is not destroyed by decoherence.

We present two Euler-Lagrangian simulation methods for particles immersed in fluids described by the Navier-Stokes equation. These implement the coupling between particle and fluid phase by (i) direct integration of the stress tensor on the particle surface discretized according to the grid topology and (ii) by a tracer particle method, which employs the volume force term in the Navier-Stokes equation to emulate “rigid” body motion. Both methods have been parallelized and applied to bulk sedimentation of about 65 000 particles (in one simulation 106 particles have been simulated). We also report results for the rheology of shear-thinning suspensions, modelled by hydrodynamically interacting particles in shear flows. Aggregation occurs due to attractive, short range forces between the particles. We also address a deficiency of the MPI communication library on the CRAY T3E which had to be resolved to improve the performance of our algorithm.

Understanding of strong earthquake motions includes the knowledge of wave propagation from source to receiver. Seismic elastic wave propagation is modelled on a large scale from the earthquake source through a heterogeneous earth to the receiver placed close to the infrastructure. Finite Difference techniques in two and three dimensions compute the full wave form solution to the wave propagation problem. The model size used in this example is 400kmx400kmx200km and source frequencies up to 2 Hz. The Finite Difference modeling software is written in High Performance Fortran and relies on on the SEPLIB processing package for Input/Ouput and parameter retrieval. A Large scale parallel machine proved to be necessary to be able to run realistic models and achieve acceptable turn-around time of modeling sequences for research purposes. The small modeling scenario in this paper demonstrates the practicality of modeling earthquake wave propagation realistically and shows that in the future it can be used in more elaborate modeling scenarios as they are planned for the Collaborative Research Project SFB 461 and other international collaborative research projects at Karlsruhe University.

In Geophysics measured seismic data sets need to be analyzed using numerical operators. Such operators consist of Fourier Transforms, integral transforms, convolutions and other mathematical concepts. The result of such inversion methods is a realistic description of the subsurface of the earth. In this project we port a seismic processing package, called SEPLIB, which has been developed at Stanford University, to a parallel environment such as the Cray T3E. This package is a cornerstone of current software development for seismic algorithms in the Geophysical Institute at the University of Karlsruhe and as such is used as a basis for other computationally intensive seismic projects. We concentrate in this article on the end user aspect of utilizing High Performance Fortran to implement geophysical seismic algorithms. We compare strategies in which the computational domain is distributed over various processors with ensembles of computational grids aligned using the HPF standard language.

The contrast mechanism in the Depolarization Near-field Scanning Optical Microscope is studied numerically. We solve the complete set of the vectorial Maxwell equations with the Green-dyade-formalism. The mathematical method and its numerical implementation are discussed in detail. First results like the polarization dependence of the image contrast are presented.

Before the year 1937 the only known concept of classifying metals, insulators and semiconductors was based on the filling of electronic bands [?,?]. On the famous Bristol conference in 1937 though de Boer and Verway [?] reported that many transition metal oxides with partially filled d-electron bands do not fit into this picture. Experiments revealed that they are either poor conductors or even insulators in spite of their partially filled bands. Soon later Peierls [?] discovered that in some special cases the electron-electron correlations arising from strong coulomb repulsion can prevent the electrons from moving thus yielding an insulator. This article founded the field of strongly correlated electrons.

Numerical simulations of the two-dimensional t-J model with one hole in the limit J/t ≪ 1 are performed for rather large systems (N ~ 10 × 10) using a world-line loop-algorithm. It is shown that in the one-hole case with J = 0, very low temperatures (ßt ~ 3000) are necessary in order to reach Nagaoka’s state. Full polarization becomes unstable for J ~ 10-4t towards partial polarization up to J/t ≲ 0.01. J/t ≳ 0.05 leads to minimal spin. The two-hole case shows enhanced total spin up to the lowest attainable temperatures (ßt = 150), well below those reached by other finite-temperature methods.

Auxiliary field quantum Monte Carlo methods for Hubbard models are generally based on a Hubbard-Stratonovitch transformation where the field couples to the z-component of the spin. This transformation breaks SU(2) spin invariance. The symmetry is restored only after summation over the auxiliary fields. Here, we analyze an alternative decomposition, which conserves SU(2) spin invariance, but requires the use of complex numbers. We show that this algorithm gets rid of the very large fluctuations observed in imaginary time displaced correlation functions of quantities which do not commute with the z-component of the total spin. The algorithm prooves to be efficient for the study of spin dynamics.

We present a Qantum Monte Carlo (QMC) study of the temperature dependent dynamics of the Kondo insulator. Working at the so-called symmetrical point allows to perform minus-sign free QMC simulations and thus reach temperatures of less than 1% of the conduction electron bandwidth. Study of the temperature dependence of the single particle Green’s function and dynamical spin correlation function shows a surprisingly intricate low temperature band structure and gives evidence for two characteristic temperatures, which we identify with the Kondo and coherence temperature, respectively. In particular, the data show a temperature induced metal-insulator transition at the coherence temperature.The theoretical description of the Kondo lattice remains an outstanding problem of solid state physics. This model, or variations of it, may be viewed as the appropriate one for understanding such intensively investigated classes of materials as the heavy electron metals[1,2] and the Kondo insulators[3]. Experimental results indicate that the electronic structures of Kondo lattice compounds undergo quite dramatic changes with temperature[4]. It is the purpose of the present manuscript to report a QMC study of the electronic structure of the so-called Kondo insulator, which shows that this model indeed undergoes a quite profound change of its unexpectedly intricate band structure as temperature increases. We are using a one dimensional (1D) ‘tight-binding version’ of the model with L unit cells and 2 orbitals/unit cell: 1$$H = - t\sum\limits_{{i,\sigma }} {(c_{{i + 1,\sigma }}^{\dag }{{c}_{{i,\sigma }}} + H.c.) - V\sum\limits_{{i,\sigma }} {(c_{{i,\sigma }}^{\dag }{{f}_{{i,\sigma }}} + H.c.)} } - {{\epsilon }_{f}}\sum\limits_{{i,\sigma }} {{{n}_{{i,\sigma }}} + } {\text{ }}U\sum\limits_{i} {f_{{i, \uparrow }}^{\dag }{{f}_{{i, \uparrow }}}f_{{i, \downarrow }}^{\dag }{{f}_{{i, \downarrow }}}.}$$ Here c _i,σ† (f _i,σ†) creates a conduction electron (f -electron) in cell i, n _i,σ =f _i,σ†f _i,σ. Throughout we consider the case of ‘half-filling’ i.e. two electrons/unit cell and, as an important technical point, we restrict ourselves to the symmetric case, ∈ _f =U/2. The latter choice, while probably not leading to any qualitative change as compared to other ratios of ∈ _f /U, has the crucial advantage that at half-filling the model acquires particle-hole symmetry, i.e. the Hamiltonian becomes invariant under the transformation α _i,σ → exp(iQ • R _i )α _i,σ†, where α=c, f and Q=(π, π,…) (this holds for bipartite lattices with only nearest relations on the f-sites become localized, and the ‘spin gap’ closes due to c-like spin excitations. While c and f electrons seem to form a coherent ‘all-electron fluid’ below the crossover temperature, the c and f-like features in the correlation functions above this temperature are decoupled. We therefore interpret this temperature as the analogue of the coherence temperature in heavy-Fermion metals. At the high-temperature crossover both, the dispersionless f-like Kondo-resonance in the single-particle spectrum and the f-like low-energy spin excitation disappear. The only remaining f-like feature in the single particle spectrum are the high-energy ‘Hubbard bands’, corresponding to the ‘undressed’ transitions f1 → f0 and f1 → f2. We therefore interpret this second temperature as the Kondo temperature of the system.The calculations were carried out on the Cray-T3E supercomputer at the HLRS Stuttgart. The QMC algorithm ran on 64 processors with different initial configurations of the ising field [15]. Communication was used to gather the results from each processor in order to perform the statistical analysis. With this scheme a total performance of 8 Gigaflops has been achieved.

The problem of spin-charge separation is analyzed numerically in the metallic phase of the one-band Hubbard model in one dimension by studying the behavior of the single-particle Green’s function and of the spin and charge susceptibilities. We first analyze the Quantum-Monte Carlo data for the imaginary-time Green’s function within the Maximum Entropy method in order to obtain the spectral function at real frequencies. For some values of the momentum sufficiently away from the Fermi surface two separate peaks are found, which can be identified as charge and spin excitations.In order to improve our accuracy and to be able to extend our study to a larger portion of the Brillouin zone, we also fit our data with the imaginary-time Green’s function obtained from the Luttinger-model solution with two different velocities as fitting parameters. The excitation energies associated with these velocities turn out to agree, in a broad range of momenta, with the ones calculated from the charge and spin susceptibilities. This allows us to identify these single-particle excitations as due to a separation of spin and charge. Remarkably, the range of momenta where spin-charge separation is seen extends well beyond the region of linear dispersion about the Fermi surface. We finally discuss a possible extension of our method to detect spin-charge separation numerically in two dimensions.

We consider the repulsive Hubbard model on a square lattice with an additional term, W, which depends upon the square of a single-particle nearest-neighbor hopping. At half-band filling, constant W, we show that enhancing U/t drives the system from a d-wave superconductor to an antiferromagnetic Mott insulator. At zero temperature in the superconducting phase, spin-spin correlations follow a powerlaw: e-ir.Q|r|-α. Here Q= (π,π) and α is in the range 1 < α < 2 and depends upon the coupling constants W and U. This results is reached on the basis of large scale quantum Monte-Carlo simulations on lattices up to 24 × 24, and is shown to be independent on the choice of the boundary conditions. We define a pairing (magnetic) scale by the temperature below which short range d-wave pairing correlations (antiferromagnetic fluctuations) start growing. With finite temperature quantum Monte Carlo simulations, we demonstrate that both scales are identical over a large energy range. Those results show the extreme compatibility and close interplay of antiferromagnetic fluctuations and d-wave superconductivity.The understanding of the interplay between d-wave superconductivity and antiferromagnetism is a central issue for the understanding of the phase diagram of High-T _c superconductors [1]. The aim of this work is to further study a model which shows a quantum transition between a d-wave superconductor and an antiferromagnetic Mott insulator. It thus enables us to address the above question. The model we consider, has been introduced in Ref. [2]. It is defined by: 1$$ H = - \frac{t}{2}\sum\limits_i {{K_i}} - W\sum\limits_i {K_i^2} + U\sum\limits_i {\left( {{n_{i, \uparrow }} - \frac{1}{2}} \right)} \left( {{n_{i, \downarrow }} - \frac{1}{2}} \right) $$ with the hopping kinetic energy 2$${{K}_{i}} = \sum\limits_{{\sigma ,\delta }} {(c_{{i,\sigma }}^{\dag }{{c}_{{i + \delta ,\sigma }}} + c_{{i + \delta ,\sigma }}^{\dag }{{c}_{{i,\sigma }}})}$$ Here, W ≥ 0, δ = ±a _x , ±a _y , and n _i,σ = c _i,σ †c _i,σ where c _i,σ †(c _i,σ ) creates (annihilates) an electron on site i with z-component of spin σ. We impose twisted boundary conditions: 3$$ {c_{i + L{a_x},\sigma }} = \exp \left( {2\pi i\Phi /{\Phi _0}} \right){c_{i,\sigma }},{c_{i + L{a_y},\sigma }} = {c_{i,\sigma }} $$We have equally shown that the energy scales at which d-wave pairing and antiferromagnetic fluctuations occur are identical. The further understanding of spin and charge dynamics, as well as the doping of the model remains for further studies.

In this work we address the problem of multiple ionization of atoms in strong laser fields (in the infrared and visible range). To this end we numerically solve the full, three-dimensional time-dependent Kohn-Sham equations for a Helium atom in a strong (780nm) laser field. Explicit density functionals for the calculation of ionization probabilities are developed. From the results, we will draw conclusions about the role of electronic correlation in the ionization dynamics and about the validity of present-day exchange-correlation potentials.

Theoretical and Computational Chemistry are relatively recent subfields of chemistry, being developped in the last few decades. Their importance is witnessed by the fact that an ever increasing fraction of papers in top chemistry journals like the Journal ofthe American Chemical Society reports results obtained from computational methods.

The electronic structure of the hydrogen molecule in a magnetic field is investigated for parallel internuclear and magnetic field axes. The lowest states with 1Σ_g, 3Σ_u, and 3∏_u symmetry are studied for a broad range of field strengths 0 ≤ B ≤ 100 a.u. As a major result we determine the transition field strengths for the crossings among these states: The global ground state for B ≲ 0.18 a.u. is the strongly bound 1Σ_g state. The crossing of the 1Σ_g with the 3Σ_u state occurs at B ≈ 0.18 a.u. while the crossing between the 3Σ_u and 3∏_u state occurs at B ≈ 12.3 a.u. Therefore, the global ground state of the hydrogen molecule for the parallel configuration is the unbound3Σ_u state for 0.18 ≲ B ≲ 12.3 a.u. The ground state for B ≳ 12.3 a.u. is the strongly bound 3∏_u state. This result is of great relevance to the chemistry in the atmospheres of magnetic white dwarfs and neutron stars.

Polymeric materials pose a challenge for Monte Carlo simulations because of the widely spread length and time scales involved. Using large scale computer simulations we investigate the interfacial structure in a partially compatible polymer mixture. The problem is studied in the framework of a coarse grained lattice model - the bond fluctuation model on the simple cubic lattice, choosing N = 32 and lattice linear dimensions L × L × D up to 512 × 512 × 64. We employ a two dimensional geometric decomposition scheme to implement this algorithm on the CRAY T3E. The algorithm scales very well with the number of processors. The structure of polymer coils near interfaces between coexisting phases of symmetrical polymer mixtures (AB) is discussed, as well as the structure of symmetric diblock copolymers of the same chain length N adsorbed at the interface. Distribution functions for monomers at the chain ends, in the center of the copolymer chain, and in the center of the individual blocks are obtained. These are compared to the predictions of the self consistent field theory. For low copolymer concentration (“mushroom regime”) the copolymer extends its blocks into the appropriate bulk phases; individual blocks are only mildly perturbed (“dumb-bell”-like). At higher copolymer concentration, the copolymer displaces the homopolymer from the interface (“dry brush”).

We present the results of a large scale computer simulation we performed to investigate the dynamical properties of supercooled silica. We show that parallel supercomputers such as the CRAY-T3E are very well suited to solve these type of problems. We find that at low temperatures the transport properties such as the diffusion constants and the viscosity agree well with the experimental data. At high temperatures this simulation predicts that in the transport quantities significant deviations from the Arrhenius law should be observed. Finally we show that such types of simulations can be used to investigate also complex dynamical quantities, such as the dynamical structure factor, and that the wave-vector and frequency range accessible is significantly larger than the one of real experiments.

CFD applications require the highest percentage of computational time on NEC SX-4 as well as on CRAY T3E within HLRS. Because of the space available only 10 project reviews could be accepted for publication in the proceedings, six of which were presented orally and four in a poster session.

Direct Numerical Simulations (DNS) of turbulent zero pressure gradient boundary layers have been performed on two high performance computers with different architectures. The one, a Cray T3E-900, is a massively parallel computer (HLRS computing center, Stuttgart/Germany). The other, a Fujitsu VPP700, is a Vector-parallel computer (Leibniz Computing Center, Munich/Germany). Both computers are well suited for large-scale flow computations. For the first time a DNS with a locally refined grid near the wall has been applied for spatially developing flows. This approach leads to considerable savings of computational time compared to a full grid simulation.

Laminar-turbulent transition induced by a harmonic point source disturbance in a flat-plate boundary layer with adverse pressure gradient is investigated by spatial Direct Numerical Simulation (DNS) based on the complete three-dimensional Navier—Stokes equations for incompressible flow. A local disturbance is introduced into the two-dimensional (2-D) base flow at the wall by a harmonic point source. Thus Tollmien—Schlichting waves of a single frequency and a large number of obliqueness angles are stimulated and propagate downstream simultaneously, undergoing amplification by primary and subsequent instabilities, and eventually lead to breakdown of the laminar flow. The development of the wave train in the boundary layer is investigated by the spectral amplitude evolution and the vorticity/shearlayer dynamics. The computational aspects of this LAMTUR project are discussed in detail for runs on the NEC SX-4 and the CRAY T3E supercomputers.

Recent applications in the field of computational fluid dynamics are presented, which were run on the NEC SX-4 of the High-Performance Computing Center of Stuttgart. External and internal flow problems were simulated. The internal flow problems include the breakdown of a slender vortex in a pipe flow and the flow in a piston engine during the intake and compression stroke. In addition, large-eddy simulations of turbulent flow through pipe bends and of turbulent jet flows are presented. All results are obtained with explicit or implicit solution schemes on block structured curvilinear grids. The number of grid points varies from 300,000 in the case of a turbulent jet to approx. 2 million in the case of the piston engine flow. All algorithms are vectorized and parallelized. Characteristic computing times and memory requirements are reported for the different applications.

The numerical study of turbulent flow in pipes is important for fundamental research and allows to solve engineering problems, too. By the use of modern supercomputers the flow through complex pipe geometries can be predicted by the Direct Numerical Simulation method, where the Navier Stokes equations are solved directly and no modelling of turbulence is required. The flow in straight, toroidal and helically coiled pipes has been investigated for the same Reynolds number Re _τ = u _τ R/v = 230. The curvature k ranges from 0 to 0.1 and the torsion τ ranges from 0 to 0.165. The influence of curvature and torsion on turbulent pipe flow is shown by surface profiles of the axial velocity, the pressure and the intensity of the velocity components perpendicular to the axial velocity.

This paper presents the parallelization of a multi-block finite-volume CFD code. A simple static computational and communicational load balancing algorithm is proposed and implemented. Measurements on an IBM RS/6000 SP System using up to 128 processors are presented for different application examples and compared to a performance model.

The fluid flow and separation behaviour between conical rotating discs in a disc stack centrifuge is studied numerically using computational fluid dynamics. The fluid flow on the one hand is calculated by a Finite-Volume-Method while the separation behaviour is obtained with a Euler-Lagrange-Method. The results of the simulation are in good agreement with experimental data.

The unsteady flow in an axial flow turbine stage with a second stator blade row is investigated by means of a Navier-Stokes code especially developed for turbomachinery applications. Due to the low aspect ratio of the blades of the test machine a highly three-dimensional flow dominated by secondary flow structures is observed. Simulations that include all blade rows are carried out. The present investigation focuses on the stator/rotor/stator interaction effects. Secondary flow structures and their origins are identified and tracked on their way through the passage. The time-dependent secondary velocity vectors and total pressure distributions as well as flow angles and Mach number distributions as perturbation from the time-mean flow field are shown in cross-flow sections and azimuthal cuts throughout the turbine. Simulations and measurements show a good overall agreement in the time-dependent flow behaviour as well as in the secondary flow structures.

The purpose of this paper is to briefly describe the BRITE/EURAM HELIFUSE project in its aims and phases, and to present the activities of the Institute for Aerodynamics and Gas Dynamics, Stuttgart University, as contractor of this project during the period 4/97 to 4/98. The project aims at evaluation and improvement of State-of-the-Art Navier-Stokes solvers for prediction of helicopter fuselage drag. The effect of grid refinement is investigated, and some steps in improving the NSFLEX code used at IAG are presented.

This paper presents results of a numerical study for unsteady three—dimensional, incompressible flow. A finite element multigrid method is used in combination with an operator splitting technique and upwind discretization for the convective term. A nonconforming element pair, living on hexahedrons, which is of order O(h2/h) for velocity and pressure, is used for the spatial discretization. The second order fractional—step—θ—scheme is employed for the time discretization.For this approach we present the parallel implementation of a multigrid code for MIMD computers with message passing and distributed memory. Multiplicative multigrid methods as stand alone iterations are considered. We present a very efficient implementation of Gauß-Seidel resp. SOR smoothers, which have the same amount of communication as a Jacobi smoother.As well we present measured MFLOP for Blas 1 and Lin routines (as SAXPY) for different vector length. The measured performance are between 20 MFLOP for large vectorlength and 450 MFLOP for short vectorlength.

The goal of this work is the development of a parallel software-platform for solving partial differential equation problems. State-of-the-art numerical methods have been developed and implemented for the efficient and comfortable solution of real-world application problems. Emphasis is laid on the following topics: distributed unstructured grids, adaptive grid refinement, derefinement/coarsening, robust parallel multigrid methods, various FE and FV discretizations, dynamic load balancing, mapping and grid partitioning. Some important application examples will be presented including structural mechanics, two-phase flow in porous media, Navier-Stokes problems (CFD) and density-driven groundwater flow.

Design and optimization of industrial processes and equipments have been based on pure empirical and experimental experience for many years. Now, because of the enormous improvement of hardware resources like parallel computers and algorithmical tools, we are able to study complex multidimensional industrial processes by simulation, and to develop a new platform for the fundamental understanding of problems with high complexity and for the optimal design of industrial systems. The response time for realistic simulations is now of an acceptable order, such that extensive parameter studies can be performed. The fascinating progress in hardware resources and algorithmical tools require further research for combining both. E. g. the dynamical load balancing is still an area which has to be improved.

Direct numerical simulations (DNS) have become one of the most effective tools to investigate turbulent combustion. To further improve our knowledge about the fundamental interaction processes between turbulent transport and chemical reactions using DNS, it is necessary to include detailed chemical reaction schemes. This leads to an enormous demand of computational power, which can only be provided by the fastest supercomputers available. Therefore, we developed a code for the direct simulation of chemically reacting flows on massively parallel computers. We utilize this code to investigate the interaction of H₂/O₂/N₂ flames with decaying turbulence.

A validation exercise is presented with the objective of demonstrating that using a mature furnace simulation tool on high end supercomputers enables the reliable prediction of coal-fired utility boiler performance within short time frames. The tool used in the present investigation is the in-house developed 3D-furnace simulation code AIOLOS. To prove the predictive capabilities of AIOLOS the code is applied to the numerical simulation of three different industrial furnaces differing in the firing concepts, sizes and fuels. The discretizations range from 100,000 to 2,000,000 computed cells. Numerical predictions of AIOLOS are validated with measurements of temperature, wall heat fluxes, carbon in fly ash, and species concentrations provided by the industrial partners ENEL, Saarberg and RWE. The comparison of measured and calculated values showed that predictions with AIOLOS are accurate enough to enable the virtual optimization of combustion equipment in large scale utility furnaces. Furthermore, the vector and parallel performance of AIOLOS on the parallel vector computer NEC SX-4/32 has been assessed. The performance results showed that for the above mentioned calculations the runtime can be reduced to a couple of hours being short enough for industrial purposes.

In this chapter articles from various fields are collected, spanning from computer-science and image-processing to engineering applications from electrical engineering and structural mechanics.

This paper addresses the analysis of electromagnetic radiation and scattering problems in parallel using the method of moments (MoM) as implemented in the computer code FEKO. The parallelisation of all steps of the solution process including geometry setup, parallel computation of the matrix elements using a distributed storage scheme, solution of the system of linear equations, and near- and far-field calculations is discussed and some results concerning the achieved scalability are presented.

Development and improvement of protective clothing has always been a challenging task. New materials and innovative production processes lead to safer and more comfortable products. Because of the large number of influence parameters, optimization by experiments is time-consuming and presents numerous difficulties. Parameter studies can be conduced using computer simulation contribute substantially to development time reduction and product innovations.The explicit variant of Finite-Element-Method (FEM) for realistic simulation of mechanical properties of knitted fabrics was applied within the scope of an AIF- and DFG-project. With this method, it was possible for the first itme, to model the complex three-dimensional volume contact situations between clasping threads and account for surface friction. The simulation of the penetrating test for a wire fabric of a fencing mask illustrate the efficency of this novel method and the potential for applying the method in the field of protective clothing.

In this paper we report on the results of a joint effort of astrophysicists and computer scientists to develop and implement a parallel program that enables us to solve large systems of hydrodynamic equations and covers a wide range of applications in astrophysics. We introduce the Distributed Threads System (DTS) as an environment for the development of portable parallel applications. The numerical method Smoothed Particle Hydrodynamics (SPH) is used to simulate the viscous spreading of an accretion disk around a massive compact object as an astrophysical test problem. The SPH code was parallelized using DTS and successfully ported to systems of different architecture. The use of a parallel SPH code on supercomputers enables us to treat astrophysical systems that were not accessible before. The achieved speedup proves the efficiency of DTS as a parallel programming environment. The physical results show the consistency and accuracy of the SPH method.

Parallelisation of the watershed segmentation method is studied in this paper. Starting with a successful parallel watershed design solution, extensive tests on various parallel machines are presented to prove its portability and performance. Next, the watershed algorithm has been re-formulated as a modified connected component problem. Consequently, we present a scalable parallel implementation of the connected component problem, which is the key for the future improving of the parallel design for the watershed algorithm.

The project “Interactive Parallel Visualization in the Framework of the Sonderforschungsbereich 382” (IPV 382) is concerned with the development of visualization and steering tools for large scale applications in physics with simulations running on parallel computers.Typical examples are online visualizations of molecular dynamic simulations with up to about one billion of atoms. For the visualization of the information contained in these huge data sets direct volume visualization proved to be an appropriate tool.

This article describes the general computational tools for a new proof of the existence of the large sporadic simple Janko group J₄ [10] given by Cooperman, Lempken, Michler and the author [7] which is independent of Norton [12] and Benson [1].Its basic step requires a generalization of the Cooperman, Finkelstein, Tselman and York algorithm [6] transforming a matrix group into a permutation group.An efficient implementation of this algorithm on high performance parallel computers is described. Another general algorithm is given for the construction of representatives of the double cosets of the stabilizer of this permutation representation. It is then used to compute a base and strong generating set for the permutation group. In particular, we obtain an algorithm for computing the group order of a large matrix subgroup of GL _n (q), provided we are given enough computational means.It is applied to the subgroup G = 〈x, y〉 < GL₁₃₃₃(11) corresponding to Lempken’s construction of J₄ [11].