# Questions tagged [reference-request]

This tag is for requests for books, papers, and citations.

272 questions
Filter by
Sorted by
Tagged with
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 ...
299 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 ...
44 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 ...
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 ...
95 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-...
1 vote
44 views

1 vote
136 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?
91 views

### How to get an "optimal point" for refinement in FEM adaptive mesh refinement?

Consider the following 1D problem \begin{align*} \begin{cases} \displaystyle -\frac{d^2u}{dx^2} = f(x), \hspace{0.5cm} x\in (a,b) \\[4mm] u(a) = u_{a}, \ \ u(b) = u_{b} \end{cases} \end{align*} I ...
1 vote
169 views

39 views

### Unconstrained convex optimization: correlation between dimensionality and Lipschitz constant

The author of the SIAM News article "Optimization Theory and Perspectives on the Field of Machine Learning" mentions: ... For unconstrained convex optimization, GD (gradient descent) ...
124 views

### Has there been a comparison bewteen SIMPLE/SIMPLER and JFNK for steady CFD?

I'm looking for a comparison between the Jacobian-Free Newton-Krylov (JFNK) method performance compared to the conventional CFD nonlinear solution methodologies like SIMPLE. Does anyone know if such ...
125 views

### A priori FEM estimates without $H^2$ regularity

In basic lectures on finite elements theory, people always assume $H^2$ regularity of the solution in order to derive $O(h^k)$ a priori estimates in the norms $H^{2-k}$, $k=1,2$. For simplicity let's ...
67 views

### Reference request for finite elements theory

Consider a domain $\Omega \subseteq \mathbb{R}^{2,3}$ which is non convex and with $C^2$ boundary. Could you recommend a good reference where it is explained how: without needing isoparametric ...
3k views

### How to directly compute the inverse of an ill-conditioned dense matrix

I know that it is generally a bad idea to compute the inverse matrix directly. However, if it is necessary to compute the inverse of an ill-conditioned invertible dense matrix, then what can I try? ...
2k views

1 vote
92 views

### How to Impose nonhomogeneous Neumann Boundary Condition in the DG Formulation

Consider the following partial differential equation \begin{align} \frac{\partial u}{\partial t}+\frac{\partial f}{\partial x} &= g(x,t), \ \ x\in \Omega = [x_{L},x_{R}] \\ u(x,0) &= u_{0}(x) ...
1 vote
814 views

### Simple particle-in-cell examples

I am studying about the 1D EM-PIC (Electro Magnetics using particle-in-cell) simulation. I want to have a simultaneous time-integration of the electric/magnetic fields plus the motion of free charges ...
690 views

### FEM for vector valued problems: reference request

I'm a PhD working in a computational mechanics lab. I come from a Math department, and I have a good background for what concerns the basics of finite elements, like inf-sup conditions, DG, non-...