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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, ...
2
votes
1answer
107 views

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 ...
0
votes
1answer
32 views

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 ...
1
vote
0answers
11 views

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 ...
3
votes
1answer
27 views

Estimation of viscosity from critical properties

The above graph represents reduced viscosity as a function of reduced temperature for several values of the ...
3
votes
0answers
43 views

Large-scale optimization of nonlinear equations

I'm looking to find a computationally efficient solution to a large system of nonlinear equations. I'm trying to maximize the following function: $$ f(\vec{x}) = \sum_i^N C_i (x_i-A_i)x_i^{\epsilon_{...
3
votes
1answer
59 views

How to optimize sampling for global sensitivity analysis

What is a good way to sample parameters for performing global sensitivity analysis? Some methods are defined using integrals, some are use Monte Carlo. How do these compare?
1
vote
1answer
63 views

Prove that the set of maximizers are independent of parameter in the objective function

A maximization problem reads as $$ J(y) = \sum_{k=1}^{K} \sigma_k(y)^q \mathop{\rightarrow}^{y} max$$ where $q \in [1,\infty]$ is a user-defined parameter and functions $\sigma_k, k=\{1,\dots,K\}$ ...
-1
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0answers
8 views

How to get the best 1/f noise vs. noise floor using a low-pass filter

I'm reading in data from a system which has very high range of frequencies (MHz). I'm demodulating this signal and only interested in the 1/f noise behavior in the first few Hz of this system. Say ...
1
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0answers
28 views

Please correct my Explicit formula of Adam-Bashforth-Moulton Seventh Order

Well, actually my goal is solving ODEs with Explicit Adam-Bashforth-Moulton Seventh Order Steps with matlab code. I'm searching in the internet, and i can't find about the formula (Sadly). But if ...
0
votes
1answer
12 views

How to Collect fraction in Maple 18? [closed]

Suppose I have $$f=\frac x 3+ \frac y 3 +\frac z 3$$ And I want to use collect(f, 1/3) And I wish it will displays $$f=\frac1 3(x+y+z)$$ But it doesn't work....
3
votes
1answer
52 views

Modelling flow through pipe networks

I'm trying to educate myself on modelling solute flows through pipe networks. This is a follow up of my previous post here $$\frac{\partial C}{\partial t} = - v\frac{\partial C}{\partial x}$$ While ...
1
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0answers
29 views

How to avoid density getting “deleted” in two way rigid body coupling with LBM CFD?

I've been reading this paper recently, which talks about using Lattice Boltzmann methods and two way coupling. Specifically, it outlines fluid solid coupling, and solid fluid coupling, and how simply ...
3
votes
1answer
288 views

The Formula of Explicit Runge-Kutta Fourteen order

I need an explicit Runge-Kutta 14th order formula. If you know about some reference that discusses at least 10th order (or higher, since I'm looking for the 14th) of Runge-Kutta and there is ...
2
votes
2answers
56 views

How to understand the choice of Krylov subspace orthonormal basis?

This semester, I study the Krylov subspace iterative methods (about Ax=b) using the book H. A. Van der Vorst. Iterative Krylov Methods for Large Linear Systems, volume 13. Cambridge University Press, ...
0
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0answers
21 views

How to implement geometric multigrid using FEM?

So far, all the MG literature is regarding FDM.What changes if we use FEM techniques?How coarsening works(In FDM we reduce nodes in FEM do we reduce elements)?
1
vote
3answers
513 views

Create mesh for complicated 3D object for finite element analysis

I see images of steel connections, concrete dams, and other complicated 3D objects in papers which finite element analysis has been performed on them. My questions are: How these objects are created ...
0
votes
1answer
48 views

Is it possible to resample grid in such a way so that continuous objects remain continuous?

Suppose I rasterize a rectangle of width 2.5 gridpoints and get the values as shown: =============== | 0 | 1 | 1 | 0.5 | 0 | Now I resample that ...
1
vote
1answer
67 views

(FEM) Efficient CRS vectors evaluation using elements connectivities

What is an efficient way of evaluating the column (col_ind) and the row (row_ptr) vectors for the CRS (Compressed Row Storage) storage format using the Connectivity Array? The Connectivity Array is a ...
3
votes
1answer
58 views

Block-matrix: optimal fill-in reduction for LU factorization

Consider a square $N \times N$ block-matrix $\mathbf{A}$, where each $n \times n$ block $\mathbf{A}_{ii}$ is either a dense block or a zero-block. So, $N$ denotes the number of blocks, $n$ denotes the ...
3
votes
1answer
75 views

Compute the function between two images

Take an image $f$ with some characters on it (below, hjFu3). Let's apply a filter $h$ on it to obtain a second image $g$ where the text is not visible. Is there a way to compute what kind of filter $...
10
votes
1answer
108 views

Benchmark problems for eigenvalue reordering algorithms sought

Every real matrix $A$ can be reduce to real Schur form $T = U^T A U$ using an orthogonal similiary transform $U$. Here the matrix $T$ is quasi-triangular form with 1 by 1 or 2 by 2 blocks on the main ...
2
votes
1answer
77 views

Numerical stability in the product of many matrices

I have to calculate in numpy the matrix-product of many matrices (~400). Are there common practices to increase numerical stability? If this is relevant, the matrices are $300\times 300$ orthogonal ...
8
votes
1answer
336 views

Increasing V-cycles for constant Coarsest Grid Size and increasing Fine Grid size

Problem statement I implemented geometric multigrid for $-\nabla^{2}=f$ where $f=\frac{3\pi^{2}}{4}sin \frac{\pi x}{2} sin \frac{\pi y}{2} sin \frac{\pi z}{2}$ on $\Omega \in [0,1]$ on a unit cube. ...
-1
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2answers
50 views

How to use natural logarithm inside Expression on FENICS

I'm trying to evaluate the exact solution of heat diffusion in circular plate. I'm not able to use the natural logarithm inside expression. ...
4
votes
0answers
30 views

Complementary quadratic knapsack problem

The quadratic knapsack problem (QKP) $$\max_x x^TPx$$ $$\mathrm{s.t.}\;\;w^Tx\leq c,\; x\in\{0,1\}$$ where $P\geq0, w\geq0$ elementwise, is well studied and has existing solvers. My problem below ...
3
votes
1answer
398 views

what is the best theory/model to use for prediction in multivariate data?

I use software for pollutant propagation on rivers that takes as input a set of parameters ($p_1,p_2,\ldots,p_n$) and creates an output file which is basically a matrix where on each row the ...
2
votes
1answer
91 views

What's wrong with the **PCG and MINRES** in matlab?

Last week, I have learned the details of the robust iterative methods of PCG, MINRES, GMRES, which will converges to the exact solution $x^*$ of nonsingular system within $N$ steps for $A\in \mathbb{R}...
13
votes
1answer
3k views

Strong vs. weak solutions of PDEs

The strong form of a PDE requires that the unknown solution belongs in $H^2$. But the weak form requires only that the unknown solution belongs in $H^1$. How do you reconcile this?
-1
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0answers
26 views

gnuplot splot command analog in Paraview

I would like to plot the points contained in this file with Paraview, but can't seem to figure out how to do so. Each column in this file corresponds to a set of 2048 points on a 64x32 grid. Each ...
2
votes
0answers
26 views

Necessary information that a toplogical optimisation solver needs to collecte from a pre-processed CAD model

I am developing a solver that gets a CAD model as entry and does the topological optimisation calculation on it. My solver is inspired by the open source codes presented in literature. Since it is ...
2
votes
1answer
23 views

Find index for submatrix with maximum sum

Given an N-dimensional matrix A, I want to find an M<N dimensional index array I such ...
1
vote
2answers
88 views

Custom exponents for Lennard Jones in LAMMPS

I am trying to run an MD simulation using this generalized version of Lennard Jones. $$ U(r) = \left(\frac{r_0}{r}\right)^A -\frac{A}{B}\left( \frac{r_0}{r} \right)^B $$ However, I do not know how ...
0
votes
0answers
26 views

Windows 10 System Repair, possible to rework that software to allow usb to be used instead for computers with no dvd drive? [closed]

Since many computers today do not come with a CD Drive, am wondering if there is a way to rework the recovery software, which allowed for a system image backup using a recovery USB but it only allows ...
2
votes
1answer
129 views

How to optimize sampling for parameter estimation

I have a computer model with a number of parameters that need to be calibrated based on experimental results. It's also important to understand the sensitivity of the results to each parameter ...
2
votes
3answers
194 views

Amplitude at a given frequency in a wide band signal

Could anyone suggest the most computationally efficient method for finding amplitude at a given frequency having a noisy wide band signal. To be more specific about a task. I have some physical ...
1
vote
2answers
78 views

FVM vs FDM vs Conservative form vs Non conservative form

My question is regarding solving the conservative form and the non-conservative form of the governing-equations (GE), like continuity or the navier stokes equation, using finite difference method (FDM)...
0
votes
1answer
494 views

Finite Element Analysis for Laminated Plates with Holes or Patches

As the title says, I am trying to code in FEM a plate structure that either has a hole in one of the layers or one of the layers is made of patches of plates, rather than one whole plate. However, ...
3
votes
2answers
84 views

Solving for a vector in a linear system that is both left and right multiplied

I have a linear system where I am given 2 matrices, $A$ and $B$, and 2 vectors, $v$ and $c$, and I need to solve for the vector $x$. $A$ is $n\times n$, $B$ is $n \times n \times n$, and the vectors $...
2
votes
1answer
106 views

Some proof that linear translations and rotations of a bound-constrained function are equivalent

For example, I have a function to optimize: $$f_1(x,y) = x^2+y^2, \quad x_{lb}\le x\le x_{ub},\quad y_{lb}\le y\le y_{ub}$$ Then I apply rotation by $\theta$ plus translation by $x_0$ and $y_0$: $$f_2(...
1
vote
0answers
29 views

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 ...
1
vote
2answers
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 ...
0
votes
1answer
65 views

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 ...
3
votes
0answers
45 views

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 ...
0
votes
1answer
30 views

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? ...
0
votes
0answers
32 views

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 ...
0
votes
1answer
54 views

Reference for QR algorithm for complex matrix

I am trying to find out if the known QR algorithm to find the eigenvalues of a real matrix, which can be found in the book Fundamentals of Matrix Computations, can also be used for complex matrices ...
2
votes
1answer
71 views

Does mass balance hold in convective diffusion

I'm trying to understand how convection-diffusion equations are solved in pipe flow modules available in CFD solvers. $$ \frac{\partial C}{\partial t} + \nabla \cdot (\mathbf{v} C) = \nabla \cdot (D \...
4
votes
1answer
107 views

Complex differentiation of linear solvers

I have a linear system $$Ax=b$$ which I'm solving approximately, and I need to take the frechet derivative of x with respect to z. Were I solving the problem exactly (either analytically or to machine ...

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