»MTL4 combines a very high level of expressiveness with high performance. It allows algorithms of linear algebra to be expressed in near-mathematical notation while retaining high performance. MTL4 is one of the supported linear algebra backends in FEniCS/DOLFIN.«

Prof. Anders Logg, Simula and University of Oslo, Norway


»I'm a PHD candidate in Structural&Hydrualic Engineering at University of Bologna. My research topic is on fluid-structure interaction coupling Lattice-Boltzmann Method for fluid and Finite Element Method for solid. This email is just to thank you for the help that MTL4 has in my programs, especially for the easy way to use BLAS library and for the UMFPACK interface! Very powerful!!!«

Alessandro De Rosis, University of Bologna, Italy


»We are a small group of researchers developing a finite volume groundwater flow simulator WODA (Well Outline and Design Aid). Due to our limited human resources, we concentrate on the issues of physics, discretization, and non-linear solvers, while using the available open source libraries for other tasks whenever we can.
Sparse linear algebra is not our field of research, but it is an important building block in a code like ours. It is essential to have a fast and reliable library that performs these tasks. For this purpose we deploy MTL4, and we are very satisfied. Using a simple and intuitive interface we build our matrices and solve our systems with very little effort, and we do not even have to know how the data is stored or how the solvers work. On the other hand, the source code of MTL4 is clear and easy to read, allowing us to understand what exactly happens in the code if we want to know. The set of high-level operations is complete, offering much more than what we use, including the matrix-matrix multiplication, not found in most other sparse matrix packages. If we choose to extend MTL4, this is again easy, thanks to the C++ template technology deployed throughout the library. Finally, learning how to use MTL4 was easy and it took very little time. The mailing list already contained answers to most questions that we had, while the others were quickly answered by the helpful team of MTL4 developers.«

Dr. Dragan Vidović, advisor, Jaroslav Černi Institute for the Development of Water Resources, Belgrade,Serbia


»Linear algebra is a fundamental building block in writing scientific software. The MTL4 combines a high level interface, which allows for elegant formulations, with a high performance C++ implementation. The possibility of different back ends provides an intriguing opportunity to further improve execution speed in high performance settings.«

Dr. Philipp Schwaha, Shenteq, Bratislava, Slowakia


»With MTL4, we were able to implement linear ordinary differential equations in an easy and elegant way and the usage of MTL's sparse matrices ensured top performance. Due to the well-structured design of the MTL and its excellent implementation based on modern C++ techniques allowed for a very easy integration with our existing numerical routines for solving ODEs.«

Mario Mulansky, Universität Potsdam, Germany


»I am using mtl4 in my own projects and with some other coworkers. We are sure that MTL4 it is the best way. Thank you very much for your support in the past. In these months, I am just using my code with MTL4 support but soon I will start again to develop and generalize other algorithms using MTL4 parallel.«

Dr. Giuseppe Zagari, Università della Callabria, Italy


»At IFPEN, MTL4 permits the numeric researchers accessing sparse-matrix-vector structures of large size. Well performing and easy-to-use, it simplifies focusing on novel advanced algorithms.«

Dr. Jean-Marc Gratien, IFP Énergies Nouvelles, Paris, France



Projects (alphabetically)


FEniCS is free software for automated solution of differential equations. It provides software tools for working with computational meshes, finite element variational formulations of PDEs, ODE solvers and linear algebra. See more ...

Involved institutes and companies:

University of Chicago, Argonne National Laboratory, Delft University of Technology, Royal Institute of Technology KTH, Simula Research Laboratory, Texas Tech University, and University of Cambridge.

Fraunhofer Institute for High-Speed Dynamics, Ernst-Mach-Institute:

Simulation of highly dynamic processes using finite volume methods on moving meshes. See more....

French Institute for Petrol:

Multi-phase simulations of CO2 underground storage with finite volumes. See more....

Halcrow Yolles:

The Studio for Progressive Modeling (SPM) is an in-house multidiscipline team that collaborates with the architectural and engineering teams to resolve issues associated with complex geometrical forms. Through the SPM, specialty expertise in discrete differential geometry, topography, complex three-dimensional modeling and algorithm-driven design is brought to bear on projects or parts of projects that require a broader skill base to successfully deliver the development. See more ...

odeint at Universität Potsdam 

Odeint is a modern C++ library for numerically solving Ordinary Differential Equations. It is developed in a generic way using Template Meta-programming which leads to extraordinary high flexibility at top performance. See more ...

OPT microscopy:

Optical projection tomography (OPT) microscopy is a new technique which allows the 3D imaging of biological specimen over 1 cm across. It was initially developed with the hope of enabling accurate measurement of 3D shapes. See more...

Sarturis: Interactive Simulation:

The software system SARTURIS - developed at the institute of construction machines and conveying technology of TU Dresden - permits the interactive simulation of technical systems in virtual environments (VR systems as driving simulator). In this context, large systems of ordinary differential equations (ODE) must be solved in real time. See more...

Serbian Institute for Groundwater Resource Management:

The MTL4 application at the institute simulates density-driven groundwater flow problems with strongly discontinuous and anisotropic permeability. This requires solving two equations, one stationary diffusion equation for pressure, and one transient convection-diffusion equation for concentration. See more....


Shenteq provides software and application support and also offers training, project management, and consulting to make tasks more efficient. Their main expertise is semiconductor simulation. See more...

Stillwater Supercomputing:

Stillwater Supercomputing, Inc. designs and markets a compute accelerator for computational science. The compute accelerator is based on a specialized semiconductor device called the Stillwater Knowledge Processing Unit, or KPUTM. The KPU provides unmatched price/performance at ultra low power to expand the market for high-performance computing to the small and medium-sized enterprise. See more...

Université Grenoble 1 - Laboratoire Jean Kuntzmann

The laboratory Jean Kutzmann develops a finite elements library using modern paradigms of meta-programming and generic programming. The applications are: mechanical engineering, blood flow, flow in porous media, and similar. See more...

Università della Calabria - Laboratorio di Meccanica Computazionale (Labmec)

The activity at labmec mainly concerns structural applications and the computational methodologies regarding FEM and BEM models, analysis of slender structures, non-linear response of materials, inverse problems. See more ...

Vampir Trace

During a program run of an application, VampirTrace generates an OTF trace file, which can be analyzed and visualized by the visualization tool Vampir. See more....

ViennaCL at TU Wien

ViennaCL is a linear algebra library for computations on GPUs and multi-core CPUs. The library is written in C++ and based on OpenCL. In addition to core functionality, which is BLAS level 1-3 support and iterative solvers, ViennaCL 1.1.2 provides wrappers for convenient use with Eigen and MTL4, see more ...

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