Questions tagged [reference-request]
This tag is for requests for books, papers, and citations.
9
questions
3
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answer
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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
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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
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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
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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
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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
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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
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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.
...
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