# All Questions

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### Why matlab does not include full orthogonalization method (FOM )method?

Today, I have studyied Full Orthogonalization Method (FOM), one of the Krylov subspace method, using book Y. Saad. Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA, second edition, ...
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### Why MATLAB chooses the Householder in its built-in function gmres.m?

Recently, I have studied how to construct an orthonormal basis for Krylov subspace to solve $Ax=b$, where $A\in \mathbb{R}^{n\times n}$ is nonsingular. As we know, there are usually 4 ways to ...
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### Numerical bottlenecks

On a desktop scale computer, what are the most important bottlenecks (RAM vs. CPU, single vs. multithread) for numerical calculations? I'm specifically most interested in exact diagonalization and ...
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### Solving a 1D diffusion equation with linear and nonlinear source terms

I would like to numerically solve the following equation: $$\frac{\partial \rho (z,t)}{\partial t} = G - B(N_D \rho (z,t) + \rho(z,t)^2) + D \frac{\partial^2 \rho (z,t)}{\partial z^2}$$ with the ...
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### Estimation of viscosity from critical properties

The above graph represents reduced viscosity as a function of reduced temperature for several values of the ...
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### Tight binding model calculation with Extended Huckel Approximation

I've been reading Albright's Orbital Interactions in Chemistry. In the chapter on solids, he provided a general approach to find the band structure of a solid state system Now if we are to model a ...
72 views

### When should I write a matrix-vector function to handle the sparse matrix vector multiplication?

This semster, I have been studying the iterative methods for large sparse matrix system. But I have some questions. For large sparse matrix, we must use an economic storage to store them. The most ...
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### Multi-domain 3D Geometries for MATLAB PDE Toolbox

In principle the PDE Toolbox in MATLAB can handle multi-domain 3D geometries as noted here. This feature and the associated function geometryfromMesh were introduced in MATLAB R2018a. The associated ...
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### Methods to approximate obective function gradients from point cloud

Problem statement: Assume that I have an objective function $f(x)$ which takes as input a $D$-dimensional vector $x\in\mathbb{R}^D$, and that $f(x)$ is sufficiently smooth. Assume further that I ...
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### Produce vertex displacements from volumetric shrinkage data on unstructured meshes

I was wondering what would be an efficient way to produce compatible displacements for mesh nodes/vertices if the computed data is volume shrinkage of each element/cell in the unstructured mesh? ...
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### Fast algorithm for computing lower mode shapes and natural frequencies in MATLAB using sparse stiffness and mass matrices

I am looking for a fast algorithm for computing eigenvalues and eigenvectors from sparse stiffness and mass matrices in MATLAB. The eig(K, M) doesn't work with ...