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168 votes
8 answers
135k views

Recommendations for a usable, fast C++ matrix library?

29 votes
9 answers
2k views

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

29 votes
2 answers
5k views

Is Crank-Nicolson a stable discretization scheme for Reaction-Diffusion-Advection (convection) equation?

  • 5,279
29 votes
2 answers
13k views

Does a tiny determinant imply ill-conditioning of a matrix?

  • 3,334
27 votes
5 answers
7k views

What are the main differences between PETSc and Trilinos?

27 votes
3 answers
4k views

What is the principle behind the convergence of Krylov subspace methods for solving linear systems of equations?

  • 11.8k
23 votes
2 answers
5k views

A good finite difference for the continuity equation

  • 874
21 votes
1 answer
9k views

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

20 votes
1 answer
3k views

BDF vs implicit Runge Kutta time stepping

18 votes
2 answers
4k views

Numerically stable way of computing angles between vectors

  • 1,135
18 votes
6 answers
2k views

How to reorder variables to produce a banded matrix of minimum bandwidth?

  • 11.8k
16 votes
1 answer
254 views

Usefulness of elements with mesh-dependent stability

  • 1,876
14 votes
1 answer
1k views

Are direct solvers affected by the condition number of a matrix?

  • 771
13 votes
3 answers
10k views

Understanding the "rate of convergence" for iterative methods

  • 1,633
11 votes
3 answers
358 views

What is the current state of the art in solving higher dimensional parabolic PDEs (multi-electron Schrödinger equation)

  • 1,145
10 votes
5 answers
8k views

C++ library for numerical intergration (quadrature)

  • 258
10 votes
2 answers
469 views

Why do the shape of finite elements matter?

10 votes
2 answers
519 views

Where can I find a good reference for the stability properties of several methods of solving parabolic PDEs?

  • 3,335
10 votes
2 answers
1k views

How much regularization to add to make SVD stable?

8 votes
2 answers
481 views

Why does conjugate gradient work with this nonsymmetric preconditioner?

  • 3,013
8 votes
0 answers
698 views

Numerical implementation of the Dirichlet-to-Neumann map

  • 445
6 votes
3 answers
443 views

How to impose boundary condition with mixed derivatives?

  • 97
6 votes
2 answers
2k views

implementing higher order derivatives for finite element

  • 153
6 votes
1 answer
278 views

Why is the continuous Galerkin Finite Element Method a poor choice for the inverse problem for the Navier-Lame equation?

5 votes
2 answers
214 views

Building Gaussian-type quadrature schemes with Zernike polynomials

  • 2,001
5 votes
1 answer
204 views

Using finite element error estimators for adaptive mesh refinement

  • 1,859
5 votes
2 answers
3k views

Evaluating the surface integral in an FEM (Finite Elements Method) procedure

  • 107
5 votes
2 answers
535 views

Solving Poisson equation with current BC using FEM

5 votes
3 answers
134 views

Naming scientific output files

  • 51
4 votes
1 answer
295 views

Localization of Sub-problems in the Multiscale Finite Element Method

  • 11.8k