# All Questions

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15k views

### What is the preferred and efficient approach for interpolating multidimensional data?

What is the preferred and efficient approach for interpolating multidimensional data? Things I'm worried about: performance and memory for construction, single/batch evaluation handling dimensions ...
3k views

### What's the state of the art in parallel ODE methods?

I'm currently looking into parallel methods for ODE integration. There is a lot of new and old literature out there describing a wide range of approaches, but I haven't found any recent surveys or ...
16k views

### Fastest Delaunay triangulation libraries for sets of 3D points

Which is the fastest library for performing delaunay triangulation of sets with millions if 3D points? Are there also GPU versions available? From the other side, having the voronoi tessellation of ...
2k views

### What does “symplectic” mean in reference to numerical integrators, and does SciPy's odeint use them?

In this comment I wrote: ...default SciPy integrator, which I'm assuming only uses symplectic methods. in which I am refering to SciPy's odeint, which uses ...
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. ...
12k views

### Recommendation for Finite Difference Method in Scientific Python

For a project I am working on (in hyperbolic PDEs) I would like to get some rough handle on the behavior by looking at some numerics. I am, however, not a very good programmer. Can you recommend ...
1k views

### What is a good way to run parameter studies in C++

The problem I'm currently working on a Finite Element Navier Stokes simulation and I would like to investigate the effects of a variety of parameters. Some parameters are specified in an input file ...
2k views

### Parallel Scientific Computation Software Development Language?

I want to develop a parallel scientific computation software from scratch. I want some thoughts on which language to start. The program involves reading/writing data to txt files and doing heavy ...
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

### Parallel optimization algorithms for a problem with very expensive objective function

I am optimizing a function of 10-20 variables. The bad news is that each function evaluation is expensive, approx 30 min of serial computation. The good news is that I have a cluster with a few dozen ...
1k 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 ...
3k views

### Strong vs. weak solutions of PDEs

The strong form of a PDE requires that the unknown solution belongs in $H^2$. But the weak form requires only that the unknown solution belongs in $H^1$. How do you reconcile this?
691 views

### Is it well known that some optimization problems are equivalent to time-stepping?

Given a desired state $y_0$ and a regularization parameter $\beta \in \mathbb R$, consider the problem of finding a state $y$ and a control $u$ to minimize a functional \frac{1}{2} \...
3k 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 ...
1k views

### When should implicit methods be used in the integration of hyperbolic PDEs?

Numerical methods for solving PDEs (or ODEs) fall into two broad categories: explicit and implicit methods. Implicit methods allow larger stable timesteps but require more work per step. For ...
3k views

### What is the advantage of multigrid over domain decomposition preconditioners, and vice versa?

This is mostly aimed for elliptic PDEs over convex domains, so that I can get a good overview of the two methods.
2k views

### Can a Krylov subspace method be used as a smoother for multigrid?

As far as I am aware, multigrid solvers use iterative smoothers such as Jacobi, Gauss-Seidel, and SOR to dampen the error at various frequencies. Could a Krylov subspace method (like conjugate ...
7k views

### When should log1p and expm1 be used?

I have a simple question that is really hard to Google (besides the canonical What Every Computer Scientist Should Know About Floating-Point Arithmetic paper). When should functions such as ...
2k views

### When should I use C++ expression templates in computational science, and when should I *not* use them?

Suppose that I'm working on a scientific code in C++. In a recent discussion with a colleague, it was argued that expression templates could be a really bad thing, potentially making software ...
3k views

### PDE solvers for Drift-diffusion and related models

I'm trying to simulate basic semiconductor models for pedagogical purposes--starting from the Drift-diffusion model. Although I don't want to use an off-the-shelf semiconductor simulator--I'll be ...
32k views

### Why are Runge-Kutta and Euler's method so different?

I am solving a system of linear equations, $\underline {\dot x}=\underline A\cdot \underline x$, numerically. I have done this using the popular of methods of Euler and Runge-Kutta (RK). I have ...
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 ...
2k views

### For which statistical methods are GPUs faster than CPUs?

I have just installed a Nvidia GT660 graphic card on my desktop and, after some struggle, I manage to interface it with R. I have been playing with several R packages that use GPUs, especially ...
531 views

### Examples of PDE computations using parallelism in both space and time

In the numerical solution of initial boundary value PDEs, it is very common to employ parallelism in space. It is much less common to employ some form of parallelism in the time discretization, and ...
6k views

### Boundary conditions for the advection equation discretized by a finite difference method

I am trying to find some resources to help explain how to choose boundary conditions when using finite difference methods to solve PDEs. The books and notes which I currently have access to all say ...