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Kratos is free under BSD-4 license and can be used even in comercial softwares as it is. Many of its main applications are also free and BSD-4 licensed but each derived application can have its own propietary license. Kratos is multiplatform and available for Windows, Linux (several distros) and macOS.

c-plus-plus multi-platform openmp mpi parallel-computing fem bsd-license numerical-methods multiphysics dem kratos kratos-multiphysicsObject oriented finite element library built in Delphi for structural and thermal analysis in civil engineering.

3d civil-engineering delphi fem finite-element math mtxvecFinite Element Method Samples with C#

civil-engineering fem finite-elementOfficial git repository of Elmer FEM software

finite-element-methods finite-elements fem multiphysics fluid-mechanics structural-mechanics electromagnetics mpi parallel-computing acoustics elmergui elmersolver elmergridOpenGeoSys (OGS) is a scientific open source project for the development of numerical methods for the simulation of thermo-hydro-mechanical-chemical (THMC) processes in porous and fractured media. OGS is implemented in C++, it is object-oriented with an focus on the numerical solution of coupled multi-field problems (multi-physics). Parallel versions of OGS are available relying on both MPI and OpenMP concepts. Application areas of OGS are currently CO2 sequestration, geothermal energy, water resources management, hydrology and waste deposition. OGS is comprised of the THMC-simulator (simply referred to as OGS) and a visualization tool (Data Explorer). OGS is developed by the OpenGeoSys Community. It has to be noticed that the current OGS-6 version is under very heavy development and vivid discussion, and does not implement all functionality from OGS-5.

opengeosys ogs fem thmcFuturEye_JIT is a Finite Element Method (FEM) library for solving Partial Defferential Equation (PDE) based forward/inverse problems. Java is widely used in the industry level software and systems. The JVM's HotSpot Just-In-Time (JIT) compiler allows the speed of the Java program to approach that of a native application. FuturEye_JIT makes use of the JIT feature by generating small sized Java bytecode functions at runtime for the mathematical expressions in the definitoin of a problem. The resulting code is as efficient as hand written FORTRAN FEM code. FuturEye_JIT provides a mathematically appealing way for building functions and weak forms of a problem by using the Java operator overloading technique (https://github.com/amelentev/java-oo). Thus a concise, natrual and human friendly application programming interface (API) is provided.

jit fem pdeEfficient computations with symmetric and non-symmetric tensors with support for automatic differentiation. This Julia package provides fast operations with symmetric and non-symmetric tensors of order 1, 2 and 4. The Tensors are allocated on the stack which means that there is no need to preallocate output results for performance. Unicode infix operators are provided such that the tensor expression in the source code is similar to the one written with mathematical notation. When possible, symmetry of tensors is exploited for better performance. Supports Automatic Differentiation to easily compute first and second order derivatives of tensorial functions.

computational-mechanics tensor femThis is a repo for Finite Element resources. I have used this resources for learning (myself) or prototyping some FEM features before implement them in a bigger FEM software. Right now it counts with some wxMaxima worksheets, where the CAS (Computer Algebra System) Maxima is used to compute analytically the elements.

fem maxima cas mass-matrices jupyter-notebooks finite-elementsMirror of MFEM - a lightweight, general, scalable C++ library for finite element methods. Please use the official repository, https://github.com/mfem/mfem, to create issues and pull requests. See also the MFEM website:

finite-elements high-order high-performance-computing parallel-computing amr fem computational-science scientific-computing hpcThis a port of the 2D FEM project by Miles Macklin found here from C++/OpenGL to C# Unity. The code is not that stable and the physics can break if pushed too far but its a nice introduction to deformable bodies using the Finite Element Method. The original did also implement fracturing of the mesh but I have not fully ported that and probably wont. The project provides a few options to load the scene with various meshes and has some neat code that creates a mesh from a image.

fem deformation physics-simulation soft-body unityThe left hand-side graph shows the distribution of angles (the grid line is at the optimal 60 degrees). The right hand-side graph shows the distribution of simplex quality, where quality is twice the ratio of circumcircle and incircle radius. Centroidal Voronoi tessellation smoothing (Du et al.) is one of the oldest and most reliable approaches. optimesh provides classical Lloyd smoothing as well as several variants that provide faster convergence.

pypi mathematics physics engineering fem mesh mesh-generationThe JuliaFEM project develops open-source software for reliable, scalable, distributed Finite Element Method. The JuliaFEM software library is a framework that allows for the distributed processing of large Finite Element Models across clusters of computers using simple programming models. It is designed to scale up from single servers to thousands of machines, each offering local computation and storage. The basic design principle is: everything is nonlinear. All physics models are nonlinear from which the linearization are made as a special cases.

fem finite element method julia julia-languageModelReduction.jl is a Julia package to perform model reduction methods for i.e. multibody dynamics problems. The packcage includes model order reduction methods such as the Guyan reduction and the Craig-Bampton method. Reducing the sizes of stiffness and mass matrices of the model will greatly decrease the computation resources needed when performing dynamic analyses.

fem model reduction condensation static dynamic multibody dynamicsThe adapter was initially developed for conjugate heat transfer (CHT) simulations via preCICE by Lucia Cheung in the scope of her master’s thesis [1] in cooperation with SimScale. For running the adapter for CHT simulations refer to this thesis. The adapter was extended to fluid-structure interaction by Alexander Rusch [2]. This adapter was developed for CalculiX version 2.16. Other versions may be compatible, yet they have not been tested. Please let us know if you want to use a different version.

fem calculix multi-physics fluid-structure-interaction conjugate-heat-transfer co-simulation precice-adapter preciceThis adapter was implemented as part of the master thesis of Lucia Cheung in cooperation with SimScale. Currently, only conjugate heat transfer is supported. See the adapter documentation on the preCICE website and additional documentation in the cht/ directory.

fem multi-physics fluid-structure-interaction code-aster conjugate-heat-transfer co-simulation precice-adapter precicescikit-fem is a lightweight Python 3.7+ library for performing finite element assembly. Its main purpose is the transformation of bilinear forms into sparse matrices and linear forms into vectors. The library supports triangular, quadrilateral, tetrahedral and hexahedral meshes as well as one-dimensional problems. The library fills a gap in the spectrum of finite element codes. The library is lightweight and has minimal dependencies. It contains no compiled code meaning that it's easy to install and use on all platforms that support NumPy. Despite being fully interpreted, the code has a reasonable performance.

fem pde
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