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FreeFEM [3] FreeFEM is a free and open-source parallel FEA software for multiphysics simulations. The problems are defined in terms of their variational formulation and can be easily implemented using FreeFEM language. Written in C++. Sorbonne University [4] and Jacques-Louis Lions Laboratory [5] 4.2.1: 2019-06-06: LGPL: Free: Linux, MacOS ...
FreeFem++ is a programming language and a software focused on solving partial differential equations using the finite element method. FreeFem++ is written in C++ and developed and maintained by Université Pierre et Marie Curie and Laboratoire Jacques-Louis Lions. It runs on Linux, Solaris, macOS and Microsoft Windows systems.
The FEniCS Project is a collection of free and open-source software components with the common goal to enable automated solution of differential equations.The components provide scientific computing tools for working with computational meshes, finite-element variational formulations of ordinary and partial differential equations, and numerical linear algebra.
In mathematics, the method of characteristics is a technique for solving partial differential equations.Typically, it applies to first-order equations, though in general characteristic curves can also be found for hyperbolic and parabolic partial differential equation.
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.. The function is often thought of as an "unknown" that solves the equation, similar to how x is thought of as an unknown number solving, e.g., an algebraic equation like x 2 − 3x + 2 = 0.
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...
The ideas behind the MFS were developed primarily by V. D. Kupradze and M. A. Alexidze in the late 1950s and early 1960s. [1] However, the method was first proposed as a computational technique much later by R. Mathon and R. L. Johnston in the late 1970s, [2] followed by a number of papers by Mathon, Johnston and Graeme Fairweather with applications.
The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in boundary integral form), including fluid mechanics, acoustics, electromagnetics (where the technique is known as method of moments or abbreviated as MoM), [1] fracture mechanics, [2] and contact mechanics.
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