Category: Numerical Libraries
-
OpenRadioss
Introduction OpenRADIOSS is a software package for nonlinear and linear structural analysis. It is a solver for finite element analysis and includes support for various elements such as truss, beam, shell, and solid elements. OpenRADIOSS is an open-source software package, which means that it is free to use, distribute, and modify. It is developed and…
-
MFEM Tutorials (2) Simplest MFEM of Laplace Problem with Various Options Part B
Set up the bilinear form a(.,.) on the finite element space Set up the bilinear form a(.,.) on the finite element space corresponding to the Laplacian operator -Delta, by adding the Diffusion domain integrator. This code is the same as I explained earlier, it creates a BilinearForm object, “a”, which is used to represent the…
-
MFEM Tutorials (2) Simplest MFEM of Laplace Problem with Various Options Part A
Descriptions MFEM’s ex1 is a basic example of solving a linear elliptic PDE (partial differential equation) problem using the MFEM library. The problem is a simple scalar diffusion equation on a 2D mesh. The equation is defined as: where $u$ is the solution, $k$ is a scalar coefficient and $f$ is a source term. The…
-
Practice Eigen3 (1) Solving Cantiliver Beam Deflection Problems with Multifrontal Solver
To solve the cantilever beam deflection problem using the multifrontal solver in Eigen, you can follow these steps: Here is an example of how you can implement these steps in Eigen: To assemble the global stiffness matrix K for a one-dimensional beam using the finite element method, you can follow these steps: where E is…
-
Inverse Matrix Features for Eigen3 -(2) Multifrontal Solvers and Parallization using OpenMP
You can use the multifrontal solver in Eigen to solve linear systems of equations involving dense matrices. The multifrontal solver is a direct solver that uses the multifrontal method to factorize the coefficient matrix and solve the linear system. Here is an example of how you can use the multifrontal solver in Eigen: You can…
-
Inverse Matrix Features for Eigen3 -(1) Inverse for Dense and Sparse Matrix
To compute the inverse of a matrix using Eigen, you can use the inverse() function, which is defined for both dense and sparse matrices. Here are a few examples:
-
Sparse Matrix Tutorials for Eigen3
Eigen provides the SparseMatrix class for representing sparse matrices, which are matrices that have a significant number of zero elements. Here are a few examples of how you can use the SparseMatrix class in Eigen: Eigen provides many functions for performing operations on sparse matrices, such as matrix-vector multiplication and matrix-matrix multiplication. Here are some…
-
How to do Coordinate Transformation for points on three dimensional space using Eigen3
Eigen provides several tools for performing coordinate transformations on points in three-dimensional space. Here are a few examples of how you can use Eigen to transform points: To translate a point by a fixed vector, you can use the translation function to create a translation matrix, and then multiply the point by this matrix: To…
-
4th Order Tensor Operation by Eigen3
A tensor is a multi-dimensional array, and in Eigen, the Tensor class can be used to represent a tensor of any rank (number of dimensions). Here are some examples of operations on a 4th-order tensor (tensor of rank 4) in Eigen: 1. Creating a 4th-order tensor: 2. Accessing elements of a 4th-order tensor: 3. Performing…
-
Matrix Operations for Eigen3
Here are some examples of matrix operations in Eigen: 1. Summation 2. Subtraction: 3. Inner product: 4. Cross product: #Eigen3 #InnerProduct #CrossProduct #Summation of Matrix #Substration of Matrix