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1500 questions
11
votes
5 answers
Memory efficient implementations of partial Singular Value Decompositions (SVD)
For model reduction, I want to compute the left singular vectors associated to the - say 20 - largest singular values of a matrix $A \in \mathbb R^{N,k}$, where $N\approx 10^6$ and $k\approx 10^3$. Unfortunately, my matrix $A$ will be dense without…
Jan
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- 37
11
votes
3 answers
How should non-constant coefficients be treated with finite-volume first order upwind scheme?
Starting with the advection equation in conservation form.
$$
u_t = (a(x)u)_x
$$
where $a(x)$ is a velocity which depend on space, and $u$ is a concentration of a species which is conserved.
Discretising the flux (where the flux $f=a(x)u$, is…
boyfarrell
- 5,409
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11
votes
2 answers
Discontinuous Galerkin / Poisson / Fenics
I am trying to solve the 2D Poisson equation using
the Discontinuous Galerkin method (DG) and the following
discretization (I have a png file but I am not allowed
to upload it, sorry):
Equation :
$$\nabla \cdot( \kappa \nabla T) + f = 0$$
New…
micdup
- 115
- 1
- 5
11
votes
1 answer
Does anyone use software estimation methods in their computational science research?
At work, I essentially function as an independent consultant. For management and customers, I need to estimate the amount of time it will take to develop software as part of my computational science research. However, my time estimates are usually…
Geoff Oxberry
- 30,394
- 9
- 64
- 127
11
votes
3 answers
Poisson equation: Impose full gradient as boundary condition via Lagrange multipliers
I have a physical problem governed by the Poisson equation in two dimensions
$$
-\nabla^2 u = f(x,y), \; in \; \Omega
$$
I have measurements of the two gradient components $\partial{u}/\partial{x}$ and $\partial{u}/\partial{y}$ along some part of…
Markus
- 213
- 2
- 6
11
votes
1 answer
Are there any numerical advantages in solving symmetric matrix compared to matrices without symmetry?
I'm applying finite-difference method to a system of 3 coupled equations. Two of the equations are not coupled, however the third equation couples to both the other two. I noticed that by changing the order of equations, say from $(x, y, z)$ to $(x,…
boyfarrell
- 5,409
- 3
- 35
- 67
11
votes
3 answers
Which is computed faster, $a^b$, $\log_a c$ or $\sqrt[b]{c}$?
Which is computed faster, $a^b$ or $\log_a c$ or $\sqrt[b]{c}$? $a$, $b$ and $c$ are positive reals with $b>1$.
What kinds of algorithms will you use in the comparison? What are their complexities?
For example, when $c \equiv a^b$ or $c \approx a^b$…
Tim
- 1,281
- 1
- 12
- 27
11
votes
5 answers
Is it preferable to concentrate on studying math or computation?
Concurrent to my research on Krylov Subspace Methods, I have the option of exploring mathematics behind HPC a step ahead or the theory of computation (hardware, OS, compilers etc.).
Currently, I know both enough to just get by. For instance, I know…
Inquest
- 3,394
- 3
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- 44
11
votes
1 answer
What are the possible numerical schemes for a diffusion equation with a nonlinear reaction term?
For some simple convex domain $\Omega$ in 2D, we have some $u(x)$ satisfying the following equation:
$$
-\mathrm{div}(A\nabla u)+cu^n = f
$$
with certain Dirichlet and/or Neumann boundary conditions. To my knowledge, applying Newton's method in a…
Shuhao Cao
- 2,552
- 17
- 30
11
votes
2 answers
Find all the roots of a function in a given interval
I need to find all the roots of a scalar function in a given interval. The function may have discontinuities. The algorithm can have a precision of ε (e.g. it is ok if the algorithm doesn't find two distinct roots that are closer than ε).
Does such…
Charles Brunet
- 211
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- 5
11
votes
1 answer
in matlab, what differences are between linsolve and mldivide?
in matlab, both linsolve and mldivide are used for solving a system of linear equations, in all of determined, overdetermined and underdetermined cases.
Reading their documents, I was wondering what differences are between them? Are they using…
Tim
- 1,281
- 1
- 12
- 27
11
votes
1 answer
Integrating a harmonic function over a tetrahedron
Say I have a function $f : \mathbf{R}^3 \to \mathbf{R}$ that I wish to integrate over a tetrahedron $T \subset \mathbf{R}^3$. If $f$ was arbitrary, Gauss quadrature would be a good solution, but I happen to know that $f$ is harmonic. How much can…
Geoffrey Irving
- 3,969
- 18
- 41
11
votes
7 answers
Limitations of Density Functional Theory as a computational method?
This question arises from the need I have to prepare a lesson on the limitations of Density Functional Theory as a computational approach. I would like to know not only the limitations, but also reference texts I can use to prepare a more appealing…
Stefano Borini
- 1,599
- 3
- 16
- 20
11
votes
6 answers
Which language should I learn for computational science?
I'm entirely new to the notion of computational science, and am looking for a good starting point.
I understand that there's no objectively best language, but I'd like to learn a language that has an unarguably strong and prominent presence in…
user1299028
- 213
- 1
- 2
- 4
11
votes
3 answers
How to properly apply non-homogeneous Dirichlet boundary conditions with FEM?
In general, Dirichlet boundary conditions won't be satisfied exactly for FEM for non-homogeneous boundary conditions. The FEM codes I've seen set the degrees of freedom to interpolate the Dirichlet boundary condition but I haven't found any…
andybauer
- 476
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- 9