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How to address numerical non-associativity for parallel reduction?

A parallel reduction assumes that the corresponding operation is associative. This assumption is violated for addition of floating point numbers. You might ask why I care about this. Well, it makes ...
1k views

Are BLAS implementations guaranteed to give the exact same result?

Given two different BLAS implementations, can we expect that they make the exact same floating point computations and return the same results? Or can it happen, for instance, that one computes a ...
10k views

Do currently available GPUs support double precision floating point arithmetic?

I have run the molecular dynamics (MD) code GROMACS on a Ubuntu Linux cluster consisting of nodes containing 24 Intel Xeon CPUs. My particular point of interest turns out to be somewhat sensitive to ...
340 views

What programming strategies can I take for easily modifying algorithm parameters?

Developing scientific algorithms is a highly iterative process often involving changing lots of parameters that I will want to vary either as part of my experimental design or as part of tweaking ...
2k views

C++ Best practices for dealing with many constants, variables in scientific codes

I am developing a code to simulate fluid flow with biological substances present in the flow. This involves the standard Navier-Stokes equations coupled to some additional biological models. There are ...
703 views

20% performance penalty for a nice software design

I'm writing a small library for sparse matrix computations as a way to teach myself to make the best use of object-oriented programming. I've worked really hard on having a nice object model, where ...
2k views

Parsing protein structure data in C

My background is in genomics, but I have recently been working with problems related to protein structure. I wrote a few relevant programs in C, building my own PDB file parser from scratch in the ...
6k views

What is the general idea of Nitsche's method in numerical analysis?

I know that the Nitsche's method is a very attractive methods since it allows to take into account Dirichlet type boundary conditions or contact with friction boundary conditions in a weak way without ...
2k views

Finding a global minimum of a smooth, bounded, non-convex 2D function that is costly to evaluate

I have a bounded non-convex 2-D function which I'd like to find the minimum of. The function is quite smooth. Evaluating it is costly. An acceptable error is about 3% of the function's domain in each ...
950 views

Scripted Mesh Generation Software

I'm looking for a mesh generation software that is free and open source, provides a sane scripting interface for domain specification, works for complex geometries, can generate 2D and 3D meshes, ...
4k views

Disadvantages of common discretization schemes for CFD simulations

The other day, my computational fluid dynamics instructor was absent and he sent in his PhD candidate to substitute for him. In the lecture he gave, he seemed to indicate several disadvantages ...
329 views

Desktop software with HPC resources for back end number crunching

Our workgroup produces a desktop application that simulates building energy performance. It is a .NET application and when the user is running a lot of simulations, they can be quite time consuming. ...
368 views

Databases of results for numerical codes

In the numerical methods literature, many research papers consist of a description of a new algorithmic variation, followed by a few test problems comparing the new method with one or two existing ...
1k views

Which libraries have good high-level support for multigrid?

I'm planning to use multigrid to calulate some eigenvalues and vectors, and I noticed PETSc has high-level support for multigrid. The PETSc documentation says that this part of PETSc should not be ...
3k views

There are two general approaches to representing solutions in the discontinuous galerkin method: nodal and modal. Modal: Solutions are represented by sums of modal coefficients multiplied by a set of ...
4k views

Problems where Conjugate gradient works much better than GMRES

I am interested in cases where Conjugate gradient works much better than GMRES method. In general, CG is preferable choice in many cases of SPD (symmetric-positive-definite) because it requires less ...
4k views

Portable multicore/NUMA memory allocation/initialization best practices

When memory bandwidth limited computations are performed in shared memory environments (e.g. threaded via OpenMP, Pthreads, or TBB), there is a dilemma of how to ensure that the memory is correctly ...
2k views

Is there a good, easy-to-use, high quality open source CFD solver out there?

My thesis is on developing numerical methods for model reduction in combustion. I run my methods purely on the chemistry part of combustion simulations, and I have plenty of case studies for 0-D ...
3k views

Drawbacks of Newton-Raphson approximation with approximate numerical derivative

Suppose I have some function $f$ and I want to find $x$ such that $f(x)\approx 0$. I might use the Newton-Raphson method. But this requires that I know the derivative function $f'(x)$. An analytic ...
3k views

Should I rent computing resources, or buy my own computers

Since this question is related to computation, I decided to post here. Hopefully it will be seen as appropriate. I've just started running atmospheric and oceanic models, and I realize that I need ...
2k views

Example of a continuous function that is difficult to approximate with polynomials

For teaching purposes I'd need a continuous function of a single variable that is "difficult" to approximate with polynomials, i.e. one would need very high powers in a power series to "fit" this ...
2k views

BDF vs implicit Runge Kutta time stepping

Are there any reasons for why one should choose high order implicit Runge Kutta (IMRK) over BDF time stepping? BDF seems much easier to me as $q$ stage IMRK needs $q$ linear solves per time step. ...
5k views

uniform vs. non-uniform grid

It is probably a student level question but I can't exactly make it cleat to myself. Why is it more accurate to use non-uniform grids in the numerical methods? I am thinking in the context of some ...
5k views

Row major versus Column major layout of matrices

In programming dense matrix computations, is there any reason to choose a row-major layout of the over the column-major layout? I know that depending on the layout of the matrix chosen, we need to ...
1k views

Does Computational Science involve programming?

I read about computational science on Wikipedia, but my understanding is not very clear. Does computational science involve programming? How different is computational science from computational ...
2k views

(how to) write simulations that run faster?

I have started using python as the programming language for doing all my assignments in CFD. I have a very little experience in programming. I am from mechanical engineering background and am pursuing ...
2k views

Why can't Householder reflections diagonalize a matrix?

When computing the QR factorization in practice, one uses Householder reflections to zero out the lower portion of a matrix. I know that for computing eigenvalues of symmetric matrices, the best you ...
4k views

Finding which triangles points are in

Suppose I have a 2D mesh consisting of nonoverlapping triangles $\{T_k\}_{k=1}^N$, and a set of points $\{p_i\}_{i=1}^M \subset \cup_{k=1}^N T_K$. What is the best way to determine which triangle each ...
5k views

What are differences between 'a priori' and 'posteriori' error estimate in numerical analysis?

I have learnt about Finite Element Method (also a little on other numerical methods) but I don't know what are exactly definition of these two errors and differences between them?
997 views

Practical example of why it is not good to invert a matrix

I am aware about that inverting a matrix to solve a linear system is not a good idea, since it is not as accurate and as efficient as directly solving the system or using LU, Cholesky or QR ...
8k views

Profiling CFD code with Callgrind

I'm using Valgrind + Callgrind to profile a solver I have written. As the Valgrind user manual states, I've compiled my code with the debugging options for the compiler: "Without debugging info, ...
501 views

Are there operator splitting approaches for multiphysics PDEs that achieve high order convergence?

Given an evolution PDE $$u_t = Au + Bu$$ where $A,B$ are (possibly nonlinear) differential operators that don't commute, a common numerical approach is to alternate between solving $$u_t = Au$$ ...