Elegant Mathematics Ltd

Fluid Dynamics

Elegant Mathematics Ltd researches and develops the software for numerical simulation of the most physical effects connected with transport of matter. The spectrum of our mathematical solutions ranges from construction of solid state models, which are simulated with the Lame equation (software package EMLibHMatrix), covering the majority of convection-diffusion models, up to the solution of under- and supersonic computational fluid dynamics models, which we successfully solve using the Boltzmann equation approach (software package EMBoltzmann). All our models are based on the advanced scientific development in the field of finite elements and adaptive grids.

Elegant Solvers are exceptionally robust and are able to solve highly ill-conditioned problems, even those, which can not be solved by any other reasonable cost method (software packages EMLibSparse and EMLibIter).



Our new algorithm for the deterministic solution of the Boltzmann equation is based on the multilinear decomposition of velocity space. It enables us to compute the results with the same computational efforts like with the Navier-Stokes approach. Moreover, the simulation of the Boltzmann equation enhances considerably the accuracy of received results.

Solving problems of numerical subsonic gas dynamics for the given shape of a plane, stream speed and an attack angle, you can compute turbulence and all forces acting on the plane. Based on these results, you learn a behavior of a plane on various sites of the flight. If you provide a set of possible geometries of a plane and run the simulations for them, it is possible to foretell flight characteristics for each of them and to find the most appropriate one.

Moreover, if optimum values of force distribution, acting on a plane, are given, you can optimize a form of the wing, (software package EMLibMinimize), without constructing a large set of different wings, and carrying out tests with them.

Our algorithms are used at all stages of development of marine power plant turbines and helicopter propellers.




It is often difficult – and sometimes impossible – to foresee the right form of turbine blades. At the same time, designing and checking on the efficiency of different shapes of blades turn out to be unprofitable, since this method demands great expense of time and resources.

Based on the blade's geometry, temperature, liquid pressure, fluid stream velocity, and other provided physical characteristics, our algorithms will compute both the efficiency of accumulation, in case of power plant turbines, and the efficiency of feedback, in case of marine turbines. Thus, for each possible form of the blade you can learn its characteristics without the actual construction of expensive test experiments to find the optimum parameters.
Using our adaptive grid algorithms with moving boundaries, (software package EMLibGrid), you will obtain not only a full picture of fluid motion, but also of all forces and energy transfer that act to the boundaries. We also suggest to automate the process of search for the optimal shape of blades. Thus, it is enough to specify the criterion function (for example, the efficiency of a turbine), possible restrictions (for example, a condition for a subsonic fluid flow), and varied parameters (for example, some points of spline interpolation for all surface of a turbine blade – software package EMLibSmooth). In this case the search for the optimum design of your turbine is carried out automatically with the help of our EMLibMinimize package.

Suppose that you have the best shape of a turbine blade, it is powerful and optimal in respect to computational fluid dynamics (CFD). Then you need to have it forged with the maximal durability. Here we will help you again, solving Lame equation for non-elastic deformation, (software package EMLibHMatrix). It will allow you to choose the most effective strategy of forging the blade, reducing probability of occurrence of shifts and material defects, and to construct the turbine with the maximal durability and reliability.


Our new project deals with numerical simulations of hypersonic flows with deterministic and stochastic models for the Boltzmann equation. We solve the 3-dimensional, real-time Boltzmann equation with an adaptive grid and billion particles for the stochastic approach, and with million values of average velocities on each physical space cell for deterministic approaches. It gives a chance to carefully predict hypersonic gas flows at the speed close to space flights and strongly turbulent flows, (software packages EMBoltzmann, EMParBoltzmann and EMGPUBoltzmann). Thus, these programs make it possible to compute:
  • atmospheric entry heating of lander surfaces,
  • supersonic flow in propulsion compressors,
  • flow separation phenomenon,
and many other important physical phenomena. The mathematical model, included in the Boltzmann equations, allows simulating most of shock waves and does not distort results even in high Mach numbers.
We suggest to optimize your Ram-, and Scramjets by means of simulating combustion process based on the three-dimensional Boltzmann equation.

For the accurate simulation we offer you a wide range of mesh generators and proper simulation algorithms, as follows:
  • tensor uniform grids with Toplitz matrices and fast Fourier transformation,
  • tensor nonuniform grids with Kronecker matrices,
for velocity space simulations (software package EMLibMDD);
  • adaptive grids with tetrahedral finite elements of first and higher orders,
  • mesh-free and dual mesh approaches based on the Delaunay tessellation,
for the discretization of physical space (software package EMLibGrid);
  • 3D high-order finite elements
for the best approximation of boundary elements (software package EMLibGrid).

Wave Simulation

Direct Wave Simulation Problems:

I. Numerical Simulation of Magnetostatics for Prediction of Electro- and Magnetic Field Around Solenoids

This modeling allows to predict parameters of a magnetic field of any form of the magnetic coil or superconducting solenoid without gathering the test stand.
In case you make the challenge with different model parameters, for example, proportions of dimensions of the solenoid, number of coils, etc., – you can find optimum values of these parameters concerning the efficiency or other required characteristics. The test stand assembly is often rather labor-consuming and financially unprofitable. In some cases such a stand is impossible to be constructed because the customer can afford to construct only one device with expected properties. For such cases numerical modeling and optimization of parameters of the device are carried out before this device is designed.
We also provide you with self-acting searching algorithm for the best device.s Thus, it is enough to specify the objective function (for example, the efficiency), varied parameters (for example, thickness of a wire, number of coils in the solenoid), and ranges of their values. In this case, the search for the optimum design of your device will be made automatically for you by our package EMLibMinimize.

We use modern BEM-FEM coupling algorithms for simulation. The boundary element method (BEM) is used for the simulation of magnetic parts, and the finite element method (FEM) for isolators. As we need to move magnetic parts, we do not recalculate the BEM matrix, thus, it reduces numerical errors that occur in FEM during remeshing. It allows us to solve most effectively and precisely the systems with moving parts, for example, rotation of the core of an electromagnet, movement of an electromagnetic valve, and many other similar problems.

II. Numerical Modeling of Radars and Radar Invisibility


For the successful simulation of stealth properties, or optimization of radar antennas, one need to discretize large volumes of physical space with a very fine grid, so the grid step size would be considerably smaller than the wave length. It leads to huge systems of linear equations. The system matrix in these equations is often so large, that it does not fit the main memory of the modern computer. Therefore we have developed for you parallel implementations of these algorithms (software packages with labels MPP and GPU), as well as the algorithms with effective disk memory usage (software packages with labels Out-of-Core).

Here we are using the last achievements in the numerical linear algebra developed by our company. These methods allow to solve sparse unstructured linear equation systems (software package EMLibSparse), and structured linear equation systems (software package EMLibMDD). So, systems of linear equations with several millions of unknowns are solved in a few seconds on a notebook; and systems of linear equations with several billions of unknowns are solved within a reasonable time in a small Linux cluster.


The software package LRA_CDENSE of the predecessor company Elegant Mathematics Inc was used by Lockheed Martin Concern for radar invisibility of stealth aircrafts. The relative wave number in these problems exceeded 500. Now you can make this simulation using our new improved packages EMLibIter, EMLibSparse, EMLibHMatrix on workstations, and with the EMParLibIter, EMParLibSparse packages on massively-parallel computers.

The experience obtained over the last 17 years in software development for the solution of ill-conditioned linear systems allows us to take part in the radar antennas development for the most aerospace applications.

3D Inverse Maxwell Solutions

I. Ultrasound Non-Destructive Diagnostics, Tomography, Acoustic Geological Exploration and Upstreaming


We will help you to find a three-dimensional structure of the mineral distribution if only a few emitters and targets of sound waves on the surface are available, and the studied object has considerably larger dimensions than the wave length.
The current problems can be divided into two basic classes:
  • The studied object is between sources and detectors, and wave reflection from heterogeneity of the object is not considered. Common applications here are those of medical tomography and, partially, ultrasonic non-destructive diagnostics of materials.
  • Sources and receivers are situated in such a way, that waves from sources are reflected on heterogeneity of the studied object and registered by receivers. Common applications are problems of seismic prospecting of oil- and gas-fields, and some applications of ultrasonic not-destructive diagnostics of materials.
As this method does not describe wave interference, its use is limited by the condition, that the studied object should have much greater sizes than the characteristic wave length of radiation (software package EMInverse).

The basic complexity of the solution lies in the correct discretization and solution of huge ill-conditioned linear system. The discretization is carried out by finite elements of first order, so the size of each element corresponds approximately to the average size of heterogeneity in the position where the corresponding finite element is situated.

In case we have no a priory information about heterogeneity distribution, we can start calculations with a regular finite element grid, and later, try to improve the grid according to computed properties using the Voronoi-Delaunay approach (software package EMLibGrid). It allows to improve the accuracy of computation, to reduce the total amount of unknown parameters, to save computational time and reduce memory requirements (software packages EMLibIter and EMLibSparse).

Our company has 17 years experience of development of iterative methods for the solution of linear systems of equations that allows us to find the most suitable and steady method of the solution of linear systems and, if necessary, to apply a correct regularization to a singular matrix (software package EMLibIter).

II. Ground Penetrating Radars and Upstreaming


We will help you to find the structure of a three-dimensional object using interference, non-stationary time distribution of sound and electromagnetic waves.

Solving this mathematical problem, you can predict a distribution of petroliferous stratum on the basis of seismic prospecting, and simultaneously conduct correction of drilling. Our algorithms were successfully applied for numerical modeling of distribution of petroliferous stratum, and for correct direction of oil drilling. Sources and receivers of electromagnetic signals were placed on the drill and allowed "to see" the end of a petroliferous stratum already 5-7 meters before, without drilling a dead rock.
For the solution of this problem we use a new method with two different discretization grids. The first grid is used for distribution of electromagnetic waves, it is structured and fine, to make better approximation for physical phenomena of the Maxwell equations. The second grid is used for dielectric permeability approximation, and this grid is based on the 3D adaptive Voronoi-Delaunay tessellation. This dual grid approach allows describing magnetic and electric fields with minimum complexity. At the same time, adaptive grid, on which dielectric permeability is calculated, does not overload the system of equations with excessive unknown variables.

The software packages of Elegant Mathematics run on supercomputers in the High-Performance Supercomputing Center in Maui of Hawaii (USA) on behalf of Mobil Oil Corporation for the solution of ill-conditioned sparse problems with billion unknowns (software package A_SPARSE_T3D – the predecessor of our EMParLibIter and EMParLibSparse software packages).

Nowadays, our algorithms, (software package EMMaxwell), solve 3D inverse ground penetrating radar problems.

Signal Processing

Elegant Mathematics Ltd has several successful approaches for image and video stream compression based the modern Multilinear Adaptive Cross Approximation method. It can increase the compression ratio for video streams, and it is very effective for noise reduction. Using the new numerical method together with the ultra-broadband lenses, we can construct a 3D surface of a pictured object and give the information about materials over its surface.

If there are some pictures of the object, which were made from different points, a new picture of this object at an arbitrary point can be attained, provided that this point is not far from an effective central distance. This method allows substantial simplification of air and space admission: while flying past the object, it is sufficient to make a photo of the desired object only from a few points. Then, using our algorithm based on the EMLibMDD software package, you can restore the picture of the object from any other desired point, and even its 3D surface.

These algorithms can be used also for recognition of flying objects by fragmentary picturing from the ground and comparing them with the picture in the data base. In this case, we do not need to have all possible pictures of the flying object from all possible points in the data base.

We have a wide experience of work with various computer architectures from Embedded Systems up to TOP 1 supercomputers. If necessary, we are ready to transfer our algorithms on your built-in microprocessors, or to offer you a complete solution using the microprocessors of our partners. Successful results in this area are shown with our software package EMGPULibMDD, which was ported to NVIDIA 2xx and Tesla GPU processors.

Nanotechnology

Elegant Mathematics Ltd successfully develops and introduces numerical algorithms for biology, biochemistry and nanoscience.

Our new solution methods as to the Schroedinger equation and its Hartree-Fock approximation and electron density theory are widely used for semiconductor design.

Similar algorithms are developed for exact calculation of electronic density and prediction of a chemical activity of molecules.

Carrying out scientific researches at the level of microcosm of molecules, we try to describe our macrocosm more precisely. So, for example, computing a volume integral of collision energy of molecules, we are able to find out the precise form of the collision kernel in the Boltzmann equation. The last is used for the solution of computational fluid dynamic problems (software package EMBoltzmann).

Already for more than ten years, our multilinear decomposition solver (software package EMLibMDD) has been computing pure fluorescence spectra and relative concentrations of separate substances on the basis of several fluorescence spectra of different mixes without reference spectra. The similar method can be applied in a high-performance liquid chromatography.

Our multilinear decomposition algorithms are applied for increasing accuracy of protein analysis based on nuclear magnetic resonance.

Joint scientific research of Elegant Mathematics Ltd and Scandinavian National Center (Goteborg, Sweden) in the field of signal processing of nuclear magnetic resonance data has no analogues, its results were honored with being published in Nature.





EMLibIter

The software library is developed for iterative solutions of linear systems and eigenvalue problems. This package contains CG, GMRES, GMRESF, NGMRES, BiCGStab algorithms for the linear system solutions, and Lanczos, Arnoldy and Davidson methods for eigenvalue problems. All these implementations allow you to apply any external preconditioner and Newton acceleration technique.

Free CUDA CG! Take advantage from our full featured 150GFlop/s
Conjugated Gradient CUDA and CPU solvers for float, double and quad precision for free.

Optimized for Multi-Core, Vector-Pipeline, Out-of-Core, GPU and MPP; complex numbers support.

Multi-Core – symmetric multi-core multi-processing architectures, for example, Xeon Quad Core;
Vector-Pipeline – vector-pipelined processors and instructions, for example, processors with SSE2 instruction sets;
MPP – massively-parallel distributed memory computer systems, for example, Linux Clusters;
GPU, Cell – co-processors and powerful graphic cards of NVIDIA and Cell IBM;
Out-of-Core – special mathematical algorithms, which allow to use a hard disk memory as a main memory without large slowdown of computations.

EMLibSparse

The software library is developed for solutions of large sparse linear systems and eigenvalue problems. This package contains all iterative methods of the EMLibIter package. The wide range of preconditioners allows to considerably reduce computational costs. The package contains several incomplete LU and Cholesky preconditioners with optimal thresholds for neglecting preconditioner entries. To reduce computational expenses such algorithms can be implemented as of maximum degree, approximate maximum degree, nested dissection, minimal Schur complement norm and optimal permutation.

Free CUDA CG! Take advantage from our full featured 150GFlop/s
Conjugated Gradient CUDA and CPU solvers for float, double and quad precision for free.

Optimized for Multi-Core, Vector-Pipeline, Out-of-Core and partially for MPP; complex numbers support.

Multi-Core – symmetric multi-core multi-processing architectures, for example, Xeon Quad Core;
Vector-Pipeline – vector-pipelined processors and instructions, for example, processors with SSE2 instruction sets;
MPP – massively-parallel distributed memory computer systems, for example, Linux Clusters;
GPU, Cell – co-processors and powerful graphic cards of NVIDIA and Cell IBM;
Out-of-Core – special mathematical algorithms, which allow to use a hard disk memory as a main memory without large slowdown of computations.

EMLibHMatrix

The software library is developed for solutions of dense linear systems and eigenvalue problems. This package contains all iterative methods of EMLibIter package together with the complete set of H-Matrix arithmetic. It allows to create, multiply, add up, solve systems with hierarchical matrices, using direct and iterative methods with hierarchical preconditioners.

Free CUDA CG! Take advantage from our full featured 150GFlop/s
Conjugated Gradient CUDA and CPU solvers for float, double and quad precision for free.

Optimized for Multi-Core, Vector-Pipeline, Out-of-Core and partially for MPP; complex numbers support.

Multi-Core – symmetric multi-core multi-processing architectures, for example, Xeon Quad Core;
Vector-Pipeline – vector-pipelined processors and instructions, for example, processors with SSE2 instruction sets;
MPP – massively-parallel distributed memory computer systems, for example, Linux Clusters;
GPU, Cell – co-processors and powerful graphic cards of NVIDIA and Cell IBM;
Out-of-Core – special mathematical algorithms, which allow to use a hard disk memory as a main memory without large slowdown of computations.

GPU Iterative Linear System Solvers

An average performance of CG, BiCGStab, Lanczos with real arithmetic equals to 7 GFlop/s on a single NVIDIA 260. This performance is achieved from 100,000 unknowns. A complex version of these iterative methods increases twice, 14 GFlop/s. It is almost 50 times faster than on the Quad-Core Xeon 2.6 GHz processor with 666 FSB, which can deliver only 100 MFlop/s.

The main reason of our achievements lies in the comprehensive usage of fast GPU memory.
Block versions of CG [1,2], BiCGStab, GMRES/FGMRES/NGMRES [3], Arnoldy and Davidson algorithms provide even faster performance. In particular zGMRES with 10 simultaneous right hand sides achieves 70 GFlop/s on NVIDIA 260; so it is almost the peak performance of double-precision arithmetic. The similar algorithm on the Quad Core Xeon 2.6 GHz processor with 666 FSB produces only 3 GFlop/s.

Our Kronecker Preconditioner and Kronecker sparse matrix multiplication algorithm [4,5] show the incredible 250 GFlop/s on one NVIDIA GPU 260!

Free CUDA CG! Take advantage from our full featured 150GFlop/s Conjugated Gradient CUDA and CPU solvers for float, double and quad precision for free:
EM-Free-CG.zip.
  • Nikishin A., Yeremin A. Variable block CG algorithms for solving large sparse symmetric positive definite linear systems on parallel computers. I. General iterative scheme. SIAM J. Matrix Anal. Appl. 16(4), 1995, 1135-1153.
  • Nikishin A., Yeremin A. An automatic scheme for regulating the block size in the block conjugate gradient method for solving linear systems. Zap. Nauchn. Sem. POMI, 2000, J. Math. Sci., 114(6), 2003, 1844-1853.
  • Kharchenko S., Yeremin A. Multiplicative correction of a matrix on a sequence of subspaces. I. Basic algorithms and theory for the general non symmetric sign-indefinite case. Zap. Nauchn. Sem. POMI, 2002, J. Math. Sci., 121(4), 2004, 2546-2575.
  • Ibraghimov I. Application of the three-way decomposition for matrix compression. Numer. Lin. Alg. Appl. 2002; 9:551-565.
  • Ibraghimov I., Sublinear Complexity of Krylov Subspace Method for the Kronecker Product Matrices. In press in Numer. Lin. Alg. Appl, 2009.

Fast GPU Multilinear NMR Deconvolution

The multilinear decomposition has been recently approved as a new robust method for data processing of multidimensional Nuclear Magnetic Resonance. These results were published in "Nature". The application problem has so huge sizes, that modern workstations need several days to find a solution.
A new high performance implementation of this algorithm for the GPU NVIDIA 2xx stream processors is presented.

The algorithm is based on sparse implementation of parallel factor decomposition algorithm (PARAFAC) that performs alternate sparsely defined least squares minimization.

The nuclear magnetic resonance (NMR) data are usually huge and have a large amount of data entries. To handle them one needs to solve several (often hundreds) almost nonoverlapping regions with a considerably small rank, and then to make a final tune of the total large rank system.

This package allows to compute large regions independently using all power of NVIDIA GPU.

This part often shows significant slow down in the CPU architecture since it requires solving a lot of small problems where CPU cannot show all power.

Since these parts are multithreaded over NVIDIA multiprocessors, it gives us high performance improvement. The only bottleneck in this part is load balancing, however, it is not very important with usage of large data sets. Hence, with data sets published in the articles below, we reached 50-60 times speedup.

The final solution of the joined multidimensional problem with a large rank (often about 1,000 components) was again efficiently implemented, and showed us improvement 30-40 times as much as before compared with Quad Core Xeon workstations.

The core solver of mddnmr distributed by Goteborg University was originally developed by Dr. Ibragimov in 2003 when he was on the University of Saarbruecken position. Right now this package is not supported. Please, consider our fully supported EMLibMDD package instead.
  • Jaravine V., Ibraghimov I., Orekhov V. Removal of a Time Barrier for High-Resolution Multidimensional NMR Spectroscopy. Nature Methods 3(8):605-607, 2006.
  • Jaravine V., Zhuravleva A., Permi P., Ibraghimov I., Orekhov V. Hyperdimensional NMR Spectroscopy with Nonlinear Sampling. JACS 130(12):3927-3936, 2008.

Consulting

Our company develops software packages for the solution of industrial problems, where we often need to use a huge computer power: massively-parallel, vector-pipeline processors, and out-of-core solutions.

We work out the detailed task description for each customer, and then proceed to solve the challenges in the most effective and fast way. We help the customer to find the solution that best fits the available computer facilities. In case you are deciding what computer hardware to buy, we can help you to make this choice and optimize the price/performance ratio for these particular needs.

When our programs are used, we shall always accompany you and solve together your problems. You will never encounter problems with our software as we shall provide training and advise you on using our products.

We keep abreast of the quickly developing computer industry – many our algorithms are ported on such special hardware platforms like Tesla and 2xx GPU of NVIDIA and AMD-ATI. Based on broad experience on all possible massively-parallel and vector-pipelined platforms that have existed in the world since the end of the last century, we are ready to develop and optimize our algorithms for your actual computer resources.

Our algorithms allow solving problems by means of massively-parallel computers. If you have a computer with 1,000 processors, we solve your problem practically 1,000 times faster.

If your problem is so complex, that your computing facilities do not manage to solve it in a reasonable time, we will try to solve it on our facilities or to place an order for computational time in the leading supercomputer centers.

In case usage of the main memory is the most critical part of modeling, we offer our out-of-core solutions, which almost do not slow down our algorithms, allowing you to expand your main memory to the size of a hard disk.

Elegant Mathematics Ltd hopes for a successful co-operation with you!

Massively-Parallel and Multi-Core Consulting

Our company develops software packages for the solution of industrial problems, thereto we often need to use a huge computer power: massively-parallel, vector-pipeline processors, and out-of-core solutions.

We work out the detailed task description for each customer, and then proceed to solve the challenges in the most effective and fast way. We help the customer to find the solution that best fits the available computer facilities. In case you are deciding what computer hardware to buy, we can help you to make this choice and optimize the price/performance ratio for these particular needs.

When our programs are used, we shall always accompany you and solve together your problems. You will never encounter problems with our software as we shall provide training and advise you on using our products.

We keep abreast of the quickly developing computer industry – many our algorithms are ported on such special hardware platforms like Tesla and 2xx GPU of NVIDIA and AMD-ATI. Based on broad experience on all possible massively-parallel and vector-pipelined platforms that have existed in the world since the end of the last century, we are ready to develop and optimize our algorithms for your actual computer resources.

Our algorithms allow solving problems by means of massively-parallel computers. If you have a computer with 1,000 processors, we solve your problem practically 1,000 times faster.

If your problem is so complex, that your computing facilities do not manage to solve it in a reasonable time, we will try to solve it on our facilities or to place an order for computational time in the leading supercomputer centers.

In case usage of the main memory is the most critical part of modeling, we offer our out-of-core solutions, which almost do not slow down our algorithms, allowing you to expand your main memory to the size of a hard disk.

Elegant Mathematics Ltd hopes for a successful co-operation with you!

Past Elegant Mathematics Activities

About Elegant Mathematics Ltd.

Elegant Mathematics was found in 1991 in the USA, (Washington State), for development and manufacture of linear systems and eigenvalue solvers for vector-pipelined and massively-parallel algorithms, that was requested by the industry of the nineties in the last century, for the solution of mathematical, physical, chemical, aerodynamic and other tasks.

Our experts worked on the newest computer facilities of that time: 32 processor vector-pipelined system Cray C90, massively-parallel computers Cray T3D-T3E with 1,024 processors installed in NASA, Cray Research Inc, and the University of Pittsburgh, on many massively-parallel clusters with IRIX, DEC, RS6000, HP, Convex processors in the Hawaiian High-Performance Center, and on a huge amount of Linux clusters worldwide.

In the beginning of the 21st century our company underwent significant changes. There came a new generation of employees, we adjusted to new industrial problems and entered the European market.

In 2006 Elegant Mathematics moved its activity to Germany where its head office is situated at the present. The staff of our company are highly qualified specialists, who received Master's and PhD degrees on graduating from the worldwide recognized universities. Our mathematicians, physicists, chemists and programmers search out new technologies and directions in the industry. The results of their research and development activities are regularly published in scientific journals, such as Nature, JACS, LAA, etc. Hence, you are assured to find the high standard of scientific knowledge at your disposal.

All our products result from the search of the optimal task solution for the customers and application of our know-how in software development. We work out the detailed task description for each customer, and then proceed to solve the challenges in the most effective and fast way. We help the customer to find the solution that best fits the available computer facilities, and to optimize the price/performance ratio for these particular needs.



Here you can download booklets about our company

24 pages, in English, 4Mb
24 Blatt, auf Deutsch, 4Mb
24 pages, en Francaise, 4Mb

Quad Precision BLAS

A software package with complete
BLAS and ATLAS functionality that allow you to make basic linear algebra subroutine with quad precision.

You do not need a hardware support of quad precision, each quad precision value is implemented as sum of two doubles a+b, and a is bigger then b*eps, where eps is machine precision.

This package is allow you to construct iterative linear system solvers and other memory bounded algorithms with high precision and very few overhead in computational time. So, many modern x86 computers run our CG and other iterative linear system solvers based on this package only two times slower, that on double precision achieving 31 decimal precision digits on a solution!

This package is also useful for hardware with no support of double precision, like 8xx and 9xx series of NVIDIA GPU graphic cards, AMD streaming processors and IBM Cell, however, for specific hardware we are strictly recommend to ask us for corresponding version.
You may download:
  • qblas1.1-src.tar.gz sources for the most Linux and Windows (Cygwin) platform with development files and examples;
  • libqblas32.a precompiled 32 bit version of this library;
  • libqblas64.a precompiled 64 bit version of this library;
  • qblas.h C Header file;
  • qblas-demo.c C test example that runs CG on quad precision.

This is open source software copyrighted by Elegant Mathematics Ltd and distributed under GNU General Public License.

In case if you want to incorporate this library or its portions into your commercial projects, you can obtain this package or any other derivatives (for example, our iterative linear system solvers) with the commercial license that you can order from Elegant Mathematics Ltd.



RADIANT (RADar Innovation ANtenna Technology) is our new ground penetrating radar with synthetic aperture antenna that can achieve very deep (up to 1 km) geologic exploration. Recent our publications about RADIANT technology:

Transmitting antenna:

  • up to 24 J energy of each pulse,
  • up to 800 Mega Watt peak performance,
  • short period of pulse: 3-300 ns depending on application,
  • 5-1500 Watt sustained power (depending on used area and local country regulations),

Receiving antenna:

  • digitize signals with up to 2.3 GHz,
  • up to 48 numerical phased array channels,
  • very bright voltage range from 3~mkV to 1 V with 14-16 bits,
  • CE confirm,
  • achieve 200 dB total dynamic range,
  • work with many emitting antennas to save the acquisition time,
  • can be situated up to 1 km from transmitters,
  • equipped with high performance computing FPGA module and GPU accelerator that achieves up to 2 TFlop/s equivalent performance (like a small supercomputer with 100-200 CPU cores),
  • compute and display 3D inverse wave propagation results.

Our Contacts

Main Office

Elegant Mathematics Ltd,
Hanauer Muehle 2,
66564, Ottweiler,
Germany

Office in England

Elegant Mathematics Ltd,
International House, 221 Bow Road,
London E3 2SJ,
United Kingdom
Tel: +49 6858 79 79 858
Email: info@elegant-mathematics.com

Legal registration numbers:
Cardiff 05975337
HRB 16570
tax payer's account number 030/146/00565
EU VAT account number DE 257663693
Customs number (EORI) DE 1753525

Our technical support and information office is always available for you. You can contact us at any time from any point of the world by our contact phones, and receive competitive guidance and consulting about our products and services in English and German languages.

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