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6
votes
2answers
293 views

changing from global to local coordinate structure

I am going to put this question on math exchange and stack exchange as well (since it doesn't really fit in any of the specific fields, I don't know which it should go in), but here is the question: ...
3
votes
1answer
192 views

High-resolution finite volume schemes for two phase flow (fields with jumps) literature sources

what other recent sources of literature on this topic would you recommend? This is where I'm starting from: Leveque's article: HRIC scheme But the related articles seem to be a bit dated (some up ...
11
votes
2answers
21k views

How to set double precision values in Fortran

Recently, I've encountered a bizarre problem with FORTRAN95. I initialized variables X and Y as follows: X=1.0 Y=0.1 Later I add them together and print the ...
7
votes
1answer
227 views

Will upgrading to a 64 bit OS help me any?

Assuming that I am running Intel MKL (BLAS, LAPACK), is there any difference in performance if I run it on a 32 or 64 bit OS? (Of course, assuming that my hardware remains the same). My processor is ...
2
votes
1answer
525 views

Polynomial Regression using Semidefinite Programming

I'm trying to design the frequency response function for a low-pass filter. I need the function to be polynomial and to fulfill the following constraints: the coefficients must sum to 1, the function ...
5
votes
2answers
262 views

Condition number of (A + cI) matrix

For given matrix $A \in R^{n\times n}$, identity matrix $I$ and constant $c > 0$ is this possible to express $cond(A + cI)$ knowing $cond(A)$ and $c$?
2
votes
1answer
61 views

Can PetscBags be used with 64 bit versions of petsc?

I was looking at the documentation for PetscBagCreate(), and it says that The size of the A struct must be small enough to fit in a PetscInt; by default ...
2
votes
2answers
746 views

Modern Computer Efficiency vs Modern Nervous Systems

I am currently working on an evolutionary system and most of what I have heard is that a computer like mine at the moment would be able to simulate a bee sized brain (not taking into account the time ...
3
votes
1answer
1k views

Solve log equations problem [SageMath]

Input var('x') solve((log((x**2 - x), 6) - log((6*x - 10), 6) == 0), x) Output [log(x^2 - x) == log(6*x - 10)] But real ...
-5
votes
1answer
1k views

Successive over-relaxation formation of heat equation?

What is the form of SOR iterative equation for the heat equation $u_{xx}=u_{t}-1$ using centered differences both in time and spatial derivatives and using Crank-Nicolson method? $$(u(x,0)=u(L,t)=u(0,...
0
votes
1answer
110 views

Space Time tradeoff [closed]

I am wondering if you can answer a math question that I require answered for an evolutionary program that I am writing. With regards to the phenomenon known as the "space-time tradeoff" (wiki it) - ...
5
votes
2answers
6k views

Is there an MPI All Gather operation for matrices?

I have a distributed matrix, in block column format. I know that I can reshape the matrix into one long vector and use an all_gatherv operation. I just wanted to avoid the trouble of having to ...
1
vote
1answer
61 views

What does PetscBagSetFromOptions() do?

I'm writing a program that uses PETSc and SLEPc, and I was looking for a convienient way to read in options from the command line. The description of ...
9
votes
3answers
531 views

Computing the characteristic polynomial of real sparse matrix

Given a generic sparse matrix $A \in \mathbb{R}^{n\times n}$ with m << n (correction: $m \ll n^2$) non-zero elements (typically $m \in {\cal O}(n)$). $A$ is generic in the sense that it has no ...
7
votes
1answer
339 views

float128 in linear algebra

Is there any paper or research concerning float128 arithmetics applied to linear algebra problems(e.g. iterative solvers, decompositions etc.)? How much benefit is really there in comparison with ...
10
votes
4answers
874 views

How can we evaluate performance of students in computational science courses?

As someone who has to teach courses in computational science, I am confronted with the age-old question: how do I evaluate the ability of the students to learn a subject that depends on applications ...
3
votes
2answers
432 views

What numerical methods are recommendable for simulating two phase immiscible fluid flow through a pipe with high capillary pressure?

I'm simulating two phase immiscible drainage (air displacing water) in a rectangular domain of size .6mm x 2.4mm (2 dimensions) using Ansys FLUENT software. I am using an implicit Volume of Fluid ...
16
votes
3answers
617 views

How should I study creating and programming HPC systems?

I'm in a field that doesn't necessarily do a great deal of HPC work, and when it does encounter it, it's often the result of researchers from other fields exploring new applications to their methods ...
0
votes
1answer
163 views

LP infeasibility

Consider the following original LP: $\mathit{min}$ c'$x$ s.t: $Ax=0 \wedge 0\le x\le 1$ . This is my original LP which has to be solved. Now, using some reductions, I reduced the original LP to the ...
5
votes
3answers
652 views

On Vanilla Preconditioners for solving dense $Ax=b$ iteratively

I am looking for preconditioners which don't assume anything about the matrix or its origins. I basically want to be able to type in the following in MATLAB and have quick solving time: ...
5
votes
0answers
440 views

Why is my lower convex hull extraction algorithm not working?

Recently, I wrote an algorithm to obtain a delaunay triangulation of a random point set in $I=[-10,10]$x$[-10,10] \subset R^2$ by projecting these points onto the 3 dimensional paraboloid $z=x^2+y^2$, ...
3
votes
1answer
71 views

2D Jacobi line maintenance?

Suppose a linear system is given $$AX=B,$$ where $A\in\mathbb{R}^{n\times n}$ is a symmetric strictly diagonal matrix, and $X, B\in\mathbb{R}^{n\times 2}$. Therefore, the 2D Jacobi iterative solver is ...
10
votes
2answers
793 views

Trace An Isoline of an Expensive 2D Function

I have a problem similar in formulation to this post, with a few notable differences: What simple methods are there for adaptively sampling a 2D function? Like in that post: I have a $f(x,y)$ and ...
14
votes
1answer
3k views

The Remez Algorithm

The Remez algorithm is a well-known iterative routine to approximate a function by a polynomial in the minimax norm. But, as Nick Trefethen [1] says about it: Most of these [implementations] go ...
12
votes
3answers
1k views

Efficient tridiagonal matrix algorithm implementation

I am solving a physical problem using implicit numerical scheme. This leads me to solving a linear equation with tridiagonal matrix. I've coded this algorithm from Wikipedia. I wonder if there is an ...
9
votes
1answer
131 views

Numerically stable algorithms for computing remainder of polynomials

Let $f, g \in \mathbb{R}[x]$ and $\deg f > \deg g$. I am looking for asymptotically fast and numerically stable algorithms for computing $f \bmod g$. In the applications intended, both $f, g$ are ...
4
votes
4answers
242 views

Determining the algorithmic complexity

A few of the iterative matrix algorithms (CG,GMRES etc.) I have authored are acting rather funny. They converge to the right answers but take abnormally long time to run. I am in the process of ...
9
votes
3answers
955 views

Iterative methods for indefinite systems without block structure

Indefinite systems of matrices appear for example in the discretization of saddle point problems by mixed finite elements. The system matrix can then be put in the form $$\begin{pmatrix} A & B^t \...
11
votes
4answers
613 views

Runge-Kutta and Reusing Datapoints

I am trying to implement the fourth order Runge-Kutta method for solving a first order ODE in Python i.e. $\frac{dy}{dx} = f(x,y)$. I understand how the method works, but am trying to write an ...
10
votes
1answer
665 views

How to assemble and solve a matrix system in parallel from values generated in different processors?

I am solving a multiscale problem using the Heterogeneous Multiscale Method (HMM). Essentially, my particular procedure uses the following iterative process: Solve many local matrix systems. ...
7
votes
1answer
678 views

Jacobi iteration to reduce the quadratic function

Given certain function $f(X)$ which is quadratic in $X\in\mathbb{R}^{n\times d}$, $$\frac{1}{2}tr(X^TAX) - tr(Y^TBX)$$ for positive definite weighted Laplacian matrices $A, B\in\mathbb{R}^{n\times n}...
9
votes
3answers
2k views

Standard format for finite element meshes

Does there exist a standard format for finite element meshes which is widely used in the industry? Thanks!
5
votes
2answers
3k views

Fast algorithms to find the eigenvalues of some matrix on intervals of interest

I am curious how to quickly compute the eigenvalues for arbitrary matrices, sparse or dense, restricted on some given interval of interest. Suppose we have an arbitrary $n\times n$ matrix $A$, ...
6
votes
1answer
457 views

Reducing degeneracy in constrained (convex) optimization problem

DISCLAIMER: I've edited the question repeatedly for clarity and to target the most relevant answer. I have the following general problem $$ \min \|h_1\cdot h_2\|^2 $$ such that $$\|g_1\wedge g_2-h_1\...
40
votes
4answers
33k views

How does the MATLAB backslash operator solve $Ax=b$ for square matrices?

I was comparing a few of my codes to "stock" MATLAB codes. I am surprised at the results. I ran a sample code (Sparse Matrix) ...
18
votes
4answers
4k views

Is there a general-purpose library for structured grid adaptive mesh refinement?

Adaptive mesh refinement (AMR) is a common technique for dealing with the problem of widely varying spatial scales in the numerical solution of PDEs. What general-purpose libraries exist for AMR on ...
6
votes
1answer
159 views

Compability conditions in domain decomposition methods

Suppose we want to solve the Poisson equation $\Delta u = f$ on a domain $\Omega$ with Dirichlet boundary conditions. One possible way to do is by a domain decomposition method. There is a condition ...
5
votes
2answers
534 views

Recommendation for a good article/book for frontal methods?

Can someone provide an article or book that explains the principle used in frontal solvers? Some examples also may help understand the frontal methods better.Thanks in advance!
10
votes
2answers
2k views

How is geometric programming different from convex programming?

How is (generalized) geometric programming different from general convex programming? A geometric program can be transformed into a convex program, and is typically solved by an interior point method....
22
votes
2answers
2k views

What simple methods are there for adaptively sampling a 2D function?

I have a two-dimensional function $f(x,y)$ whose values I would like to sample. The function is very expensive to compute and it has a complex shape, so I need to find a way to get the most ...
9
votes
2answers
13k views

Dictionaries in pseudocode

What is a good, common way to express dictionaries (= maps) in pseudocode? I.e. datastructures that basically allow to store values for keys, iterate over all key/value pairs, test for inclusion of a ...
4
votes
3answers
367 views

Overlapping communication and computation in PETSc and/or Trilinos?

I am just learning about these packages, so forgive me if this is a trivial/silly question. Our group is working re-developing our code from the ground up using modern software practices. Currently ...
6
votes
4answers
5k views

Tools for visualizing large 3D volumes

I have a sequence of 2D images (png files) encoding the partitioning (segmentation) of a large biological 3D volume. In these files, each pixel has a color, representing the 3D object the pixel ...
4
votes
1answer
616 views

Petsc not compiling c++ files

I'm having a problem where petsc is complaining about the type of PetscScalar (I get a whole bunch of errors from the c++ standard library that revolve around PetscScalar not defined). I believe it ...
6
votes
1answer
301 views

Question about the smoothing operators in multigrid methods for nonlinear PDEs

Suppose we are dealing with a nonlinear problem, say $$ A u := L u + G(u) = f $$ the nonlinearity of the operator $A$ is the polynomial type, ie, $L$ is a linear operator, and $G(u) = u^k$, or ...
3
votes
1answer
883 views

Computing a rolling quantile

An algorithm I'm writing needs to compute rolling quantiles of a time series. Currently I do this in the naive way: for a window of size W and a vector ...
8
votes
1answer
775 views

What's the right way to compare vectors in floating-point?

I know that I should use a tolerance for comparing floating point numbers. But for comparing vectors, I can think of 3 possible solutions corresponding to different distance metrics: Compare the ...
12
votes
1answer
362 views

Enumeration of graphs deriving from Delaunay tessellations in 3D

Is there an algorithm that enumerates the graphs that correspond to some Delaunay tessellation of points in 3D? If so, is there an efficient parameterization of geometries that correspond to any "...
5
votes
5answers
348 views

Will MPI continue to be a popular basis writing scalable massively parallel solvers on future many-core CPUs? [duplicate]

Possible Duplicate: What programming paradigms should I be investing in if I want my code to run on petascale machines in the future? Having entered the multi-core era (som already refers to as ...
11
votes
1answer
684 views

Computing standard errors for linear regression problems without calculating inverse

Is there a speedier way to calculate standard errors for linear regression problems, than by inverting $X'X$? Here I assume we have regression: $$y=X\beta+\varepsilon,$$ where $X$ is $n\times k$ ...

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