Questions tagged [reference-request]
This tag is for requests for books, papers, and citations.
274
questions
3
votes
1
answer
156
views
Any FEM book recommendations that focus on stability and proofs on error bounds?
Everything from descrete stability proofs for steady state and time dependent problems. energy stability, stability of mixed methods, nonlinear problems, vector valued problems in fluid/structural/EM, ...
- 506
1
vote
0
answers
60
views
Immersed Boundary FEM reference recommendation
I want to do some Fluid-Structure Interaction using the Immersed Boundary FEM.
Could you please recommend some books or lecture notes on it?
- 191
2
votes
0
answers
69
views
Solving systems of the form $y_i=UW x_i$ for $U,W$
I'm looking for pointers/examples of solving system of equations $y_i=f_W(f_U(x_i))$ for $W,U$ where
$f_M(x) \approx M x$
$U,W$ are updated simultaneously
$i\in (0, 10^{12})$
Simplest example is ...
- 2,695
2
votes
1
answer
305
views
Literature request covering Chebyshev's pseudospectral collocation method
I would like to request some literature recommendations covering Chebyshev's pseudospectral collocation method for solving space-time PDEs. It would be nice if it even contained some example problems ...
0
votes
0
answers
45
views
Which numerical method can I use to solve this system of hyperbolic PDEs?
Backround
The mathematical model I am trying to numerically solve models wave propagation inside a cylinder with specific material properties suited for dynamic loading. The cylinder's upper base is ...
2
votes
1
answer
99
views
references for optimization in the context of parameter identification with finite elements
i am performing parameter identification for a non-linear partial differential equation (elasticity) that I solve with finite elements.
My optimization problem is a non-linear least squares data-...
- 185
1
vote
0
answers
45
views
Solution to the Liouville-Gibbs equation
What would be the approach to numerically solve for $\rho(x,t)$ the following equation with some initial conditions
$$\frac{\partial\rho}{\partial t}
+\sum_{i=1}^n\left(\frac{\partial(\rho g_i)}{\...
- 397
12
votes
2
answers
2k
views
Why are systems with clustered eigenvalues easy to solve?
I came across the following slide by Theo Diamandis & Zachary Frangella on what makes the linear system $Ax=b$ easy to solve using the conjugate gradient method.
Transcription:
CG converges ...
- 2,695
1
vote
0
answers
95
views
Closed formula to diagonalize discretized (perhaps randomized) Laplacians
I was wondering whether there is a closed formula for the eigenvalues and eigenvectors of the discretized Laplacian in (edit) $[0,1]^n$ with a uniform grid, using what I imagine is a $2n+1$ stencil.
...
- 181
6
votes
0
answers
121
views
References on the theory of Petrov-Galerkin methods for more "basic" problems
In my reading on various aspects of FEM, Petrov-Galerkin methods often arise in the study of solutions of convection-dominated systems, such as Hughes' work on Navier-Stokes, or systems where optimal ...
- 2,731
1
vote
0
answers
70
views
Has the arithmetic for exotic (unsigned float with positive exponent) number format been solved?
The data type is a doubly unsigned float. This is where the value and exponent are both strictly positive. The range of this number should include $0$ and $[1, ~2^{\text{exponent}})$, skipping all ...
- 133
1
vote
0
answers
94
views
Resource to learn assembly code
I'm a PhD student in mechanical engineering and I have to perform a lot of simulations for my project. In my lab we use several well-known libraries, from FEM to machine learning. As we're doing ...
- 405
0
votes
0
answers
50
views
Efficient cutting of mesh edges
I am looking for efficient algorithms to cut a mesh along edges. I have a (half-edge) mesh and a list of inner edges that I want to cut, such that both are new boundary edges. At each vertex there can ...
- 617
1
vote
1
answer
142
views
Could you recommend some books on FEM that explain various data-structures in FEM?
I want to understand the data structure of elements, elements around elements, and so on, and various other data structures in FEM, could you please recommend some books?
- 193
5
votes
2
answers
339
views
Continuous vs discontinuous space-time FEM
What are some reasons for approximating a (e.g. parabolic) PDE using the space-time method, with continuous finite elements in time, vs discontinuous finite elements in time?
Are there e.g. ...
- 259