# All Questions

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### Transient manufacturated solution

I'm using the method of manufacturated solution (MMS) to verify a cfd code (Transient energy equations). The equations are discretised with an implicit scheme and allow large time step without any ...
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### Iterative “solver” for $x^t \Sigma^{-1} x$

I can't imagine I'm the first to think about the following problem, so I'll be satisfied with a reference (but a complete, detailed answer is always appreciated): Say you have a symmetric positive ...
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### Finite strain FEM using an existing code that solves small strain elasticity

I have an existing FEM code that solves the linear elasticity problem. I would like to use the same code for large strain rates, still using a simple material law (Saint Venant–Kirchhoff model). [The ...
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### Chebyshev and Legendre expansions

I am looking at approximating my function $f(x)$ using a Chebyshev and Legendre series and I ran into this question. Is interpolation using $n+1$ Chebyshev nodes the same as representing the ...
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### How to implement adaptive mesh refinement using conformal triangles

I am trying to implement adaptive mesh refinement for a finite element code. The code uses (at least for now) linear triangles and so when I do the mesh refinement I want the triangular mesh to remain ...
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### How can I use mass matrix in ode15s solver?

How can I use mass matrix in ode15s solver? What is the number of rows and columns in mass matrix? Where should I define this matrix?in the m.file that I define function or in the main section of ...
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### Kernel of a Sparse Matrix

Given a sparse rectangular matrix $A$ (let's say, with dimension $n,m$ and number of non-zero elements $O(n)\sim O(m)$) with entries in $\mathbb Z/2\mathbb Z$ I'm looking for a basis of the kernel as ...
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I am trying to program the pieceewise quadratic lagrange, but I have to deal with these intervals at which the point I am trying to evaluate belongs to. So, essentially you need to have an if ...
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### Find triangle which contains point on the sphere

Suppose I have a mesh of the sphere (points on the sphere and a triangulation). What is a good and efficient way to find the triangle which contains a point on the sphere (the point does not need ...
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### Why is Crank-Nicolson considered implicit in time?

From Wikipedia: Explicit methods calculate the state of a system at a later time from the state of the system at the current time, while implicit methods find a solution by solving an equation ...
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### What are the numerical methods for testing for dissimiliarity between image based probability histograms?

I have several probability distribution histograms of images that I am comparing to test for dissimilarity. Each histogram has 256 bins, the bins are common for all histograms. The images are taken ...
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