# All Questions

8,756 questions
Filter by
Sorted by
Tagged with
3k views

### Schur's Complement and Inverse of Block Matrices

Assume that we are given a block matrix of the form: $$M = \left[ \begin{array}{cc} A & b \\ b^T & c \\ \end{array} \right]$$ where $b$ is a column vector. and $c$ is a scalar. Schur's ...
2k views

### Solving a simple Ax=b system in parallel with PETSc

I am new to the PETSc package. I have a ~4000x4000 matrix A in matrix-market format and I want to get PETSc to solve this using multiple processors. I know how to solve the system on a single ...
588 views

189 views

### Where do I find data to start a graph data structure to practice on?

I am interested in learning firsthand about graph data structures but have no data to put into the database. Can anyone recommend a source for a beginner to find graph data? (Preferably a source that ...
270 views

### How to do upwinding in finite volume schemes for nonlinear equations?

In finite difference theory, you learn, that you have to use upwinding for equations with high convection, like Burgers' equation. What does the finite volume equivalent look like? What if the ...
80 views

### Conservative field mapping between two topologically disconnected surface meshes

Some background: the Front-Tracking method uses a triangular surface mesh to describe the boundary between two immiscible fluids. To deal with the breakup and coalescence of the fluid interface, ...
204 views

### Difference between Computational science and Computational X (X = some natural science or discipline)

Where is the divide between a computational scientist and a computational X (X = some natural science or discipline)? What questions could someone ask themself to decide which is the best route for ...
168 views

### How to accurately decompose positive semidefinite matrix and use the lower triangular part in linear equations

I have $n$ arbitrary $p\times 1$ vectors $x_i$, and $p\times k$ matrices $A_i$, and $n$ $p \times p$ positive semidefinite matrices $S_i$, where some (often most) of the $S_i$'s are same (for example ...
691 views

### On implementations of the complex QR decomposition

I have an mathematical theorem on the QR decomposition, which relies on the QR decomposition of an invertible square complex matrix always constructing a triangular matrix with real diagonal entries. ...
144 views

### Computing ratio of trigonometric functions

I have need to compute the functions: $$f(x) = \frac{\sin^{-1}x}{x}$$ and $$g(x) = \frac{\sin a x}{\sin x}$$ where $a\in[0,1]$ and $x\in[0,\frac{\pi}{2}]$ and is often very small ($x\ll 1$). Are ...
293 views

### Partitioning of mesh with 20 noded hexahedral elements [closed]

Is there a way to partition a mesh consisting of 20 noded hexahedral elements for parallel processing? I used METIS for partitioning mesh with 8 noded hexahedron elmements, which works fine but i don'...
194 views

### What is the most efficient approach to interpolate values between two FEM meshes in 2D?

I am looking for efficient algorithm to interpolate values from one unstructured 2D mesh grid to another. Both grids are constructed using the same type of elements (triangles or quadrilaterals). Both ...
1k views

4k views

2k views

### Magma vs. Plasma

I'm having a difficult time understanding the difference between the linear algebra packages MAGMA and PLASMA from just a quick glance. It looks like MAGMA is oriented towards GPU's and vector ...
2k views

### Flexible Mesh Framework

I am looking for flexible and easy to learn mesh framework which provides data structure for representing and manipulating meshes in 2D i 3D. I've already found a few: MSTK https://software.lanl.gov/...
3k views

### Implementing PageRank using the Power Method

I am trying to implement the PageRank algorithm described in this paper (Fig. 1). Here is the breakdown of the steps: http://www.louismullie.com/algo.png where: ...
853 views

### Numerical Integration - handling NaNs (C / Fortran)

I am dealing with a tricky integral that exhibits NaNs at certain values near zero and at the moment I am dealing with them quite crudely using an ISNAN statement which sets the integrand to zero when ...
120 views

### how to approach time zero when the equation is not defined at that point

Some background: define a process $Y_t=\frac{1}{t}\int_0^tX_sds$, where $X_t$ is a standard Brownian motion. Then I define a function $u(t,X_t,Y_t)$ and require it to be a martingale. Thus, by ...
534 views

### Poisson solver on unstructured mesh

For the 2D Poisson equation, there exist on finite difference mesh, some code taking $O(n \log(n))$ operations to solve it on a mesh with $n$ nodes. They rely on Fast Fourier Transform or Block Cyclic ...
115 views

### Are matlab C library versions backwards compatible?

I have some C++ code that links to matlab2008b. Are matlab 2012a and 2012b backwards compatible with 2008b? If it's not trivially compatible, are there some simple steps to make it compatible?