Agros2D is an open-source code for numerical solutions of 2D coupled problems in technical disciplines. Its principal part is a user interface serving for complete preprocessing and postprocessing of the tasks (it contains sophisticated tools for building geometrical models and input of data, generators of meshes, tables of weak forms for the

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s and tools for evaluating results and drawing graphs and maps). The processor is based on the library

Hermes Hermes (; grc-gre, Ἑρμῆς) is an Olympian deity in ancient Greek religion and mythology. Hermes is considered the herald of the gods. He is also considered the protector of human heralds, travellers, thieves, merchants, and orato ...

containing the most advanced numerical algorithms for monolithic and fully adaptive solution of systems of generally nonlinear and nonstationary partial differential equations (PDEs) based on

hp-FEM hp-FEM is a general version of the finite element method (FEM), a numerical method for solving partial differential equations based on piecewise-polynomial approximations that employs elements of variable size ''(h)'' and polynomial degree ' ...

(adaptive

finite element method The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...

of higher order of accuracy). Both parts of the code are written in

C++ C++ (pronounced "C plus plus") is a high-level general-purpose programming language created by Danish computer scientist Bjarne Stroustrup as an extension of the C programming language, or "C with Classes". The language has expanded significan ...

.Karban, P., Mach, F., Kůs, P., Pánek, D., Doležel, I.: Numerical solution of coupled problems using code Agros2D, Computing, 2013, Volume 95, Issue 1 Supplement, pp 381-408

Features

* Coupled Fields - With coupled field feature you can blend two or more physical fields in one problem. Weak or hard coupling options are available. * Nonlinear Problems - Simulation and analysis of nonlinear problems are available. Agros2D now implements both Newton’s and Pickard’s methods. * Automatic space and time adaptivity - One of the main strengths of the Hermes library is an automatic space adaptivity algorithm. With Agros2D is also possible use adaptive time stepping for transient phenomena analysis. It can significantly improve solution speed without decreasing accuracy. * Curvilinear Elements - Curvilinear elements is an effective feature for meshing curved geometries and leads to faster and more accurate calculations. * Quadrilateral Meshing - Quadrilateral meshing can be very useful for some types of problem geometry such as compressible and incompressible flow. * Particle Tracing—Powerful environment for computing the trajectory of charged particles in electromagnetic field, including the drag force or their reflection on the boundaries.

Highlights of capabilities

* Higher-order finite element method ( ''hp''-FEM) with ''h'', ''p'' and ''hp'' adaptivity based on reference solution and local projections * Time-adaptive capabilities for transient problems * Multimesh assembling over component-specific meshes without projections or interpolations in multi-physics problems * Parallelization on single machine using

OpenMP OpenMP (Open Multi-Processing) is an application programming interface (API) that supports multi-platform shared-memory multiprocessing programming in C, C++, and Fortran, on many platforms, instruction-set architectures and operating syste ...

* Large range of linear algebra libraries (

MUMPS MUMPS ("Massachusetts General Hospital Utility Multi-Programming System"), or M, is an imperative, high-level programming language with an integrated transaction processing key–value database. It was originally developed at Massachusetts Gener ...

, UMFPACK, PARALUTION,

Trilinos Trilinos is a collection of open-source software libraries, called ''packages'', intended to be used as building blocks for the development of scientific applications. The word "Trilinos" is Greek and conveys the idea of "a string of pearls", sugg ...

) * Support for scripting in

Python Python may refer to: Snakes * Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia ** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia * Python (mythology), a mythical serpent Computing * Python (pro ...

(advanced IDE PythonLab)

Physical Fields

Electrostatics Electrostatics is a branch of physics that studies electric charges at rest (static electricity). Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for amber ...

Electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving pa ...

s (steady state and harmonic) *

Magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...

(steady state, harmonic and transient) *

Heat transfer Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, ...

(steady state and transient) *

Structural mechanics Structural mechanics or Mechanics of structures is the computation of deformations, deflections, and internal forces or stresses (''stress equivalents'') within structures, either for design or for performance evaluation of existing structures. It ...

and thermoelasticity *

Acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...

(harmonic and transient) *

Incompressible flow In fluid mechanics or more generally continuum mechanics, incompressible flow ( isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. An e ...

(steady state and transient) * RF field (TE and TM waves) *

Richards equation The Richards equation represents the movement of water in unsaturated soils, and is attributed to Lorenzo A. Richards who published the equation in 1931. It is a quasilinear partial differential equation; its analytical solution is often limited ...

(steady state and transient)

Couplings

* Current field as a source for heat transfer through Joule losses * Magnetic field as a source for heat transfer through Joule losses * Heat distribution as a source for thermoelastic field

History

The software started from work at the ''hp''-FEM Group at

University of West Bohemia The University of West Bohemia ( cs, Západočeská univerzita v Plzni, ZČU) is a university in Plzeň, Czech Republic. It was founded in 1991 and consists of nine faculties. History The university was formed by the merger of the ''College of Me ...

in 2009. The first public version was released at the beginning of year 2010. Agros2D has been used in many publications.De, P. R., Mukhopadhyay, S., & Layek, G. C. (2012). Analysis of fluid flow and heat transfer over a symmetric porous wedge. Acta Technica CSAV, 57(3), 227-237.

References

External links

*
Group's website
{{Webarchive, url=https://web.archive.org/web/20170504052819/http://www.hpfem.org/ , date=2017-05-04 Numerical software Scientific simulation software Finite element software for Linux Computer-aided engineering software for Linux Engineering_software_that_uses_Qt University of West Bohemia