# All Questions

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### Minimize interesting objective function with knowledge of gradient nonlinearity?

I plan on using a Quasi-Newton method (L-BFGS) to minimize a non-linear objective function. $$f: \mathbb{R}^n \rightarrow \mathbb{R}$$ The gradient is kind of interesting: as the values of the ...
104 views

### Inverse problems with a discrete set of known parameters

What are the techniques on inverse problems to discover the distribution of parameters from a discrete set of values? For instance, I know that my domain where the PDE is defined is made up of ...
464 views

### Order of accuracy of FVM discretization

I've recently got interested in CFD and started a small project by solving the radial Reynoldsequation. Why the Reynoldsequation? I recently encountered it through my studies and somehow got stuck :) ...
392 views

### Optimisation of matrix exponential

I have a 7000x7000 sparse matrix (scipy), which I want to exponentiate. I've tried using scipy.sparse.linalg.expm, which works quite well for smaller matrices (takes a few seconds for a 1000x1000 ...
529 views

### Finite volume a posteriori error estimation

I'm wondering what alternatives there are to a grid convergence study to judge solution accuracy for a given grid resolution when doing steady-state RANS simulations on an automatically generated ...
158 views

### How to optimally choose points for multivariable Hermite interpolation?

I have a multi-variate, continuous function $f$ from $R^n$ to $R$, which I can query for its output for any input. I would like to create interpolation polynomial for it. In one-dimensional case ...
164 views

### Preconditioning technique for large sparse non-hermitian matrix

I am attempting to solve a computational acoustics problem that involves solving an underlying sparse matrix. The size of the problem varies with grid size (3D) and fill-in's obviously make direct ...
230 views

### Stability analysis for a hyperbolic PDE on staggered grid

I am trying to understand the stability of a finite difference equation on the staggered grid. I could understand the Von Neumann stability analysis for the collocated grid for a simple acoustic ...
168 views

### Rank-one Update to a Rank Revealing QR (RRQR) Factorization?

Suppose we are given an RRQR factorization for some matrix $A \in \mathbb{R}^{m \times n}$, $A\Pi = QR$ where $m > n$. Is there a cheap way to update $A' = A + uv^{\top}$ given this factorization?...
569 views

### Sparse matrix format and sparse-matrix sparse-matrix multiplication

I'm having some performance problems with my code dealing with the multiplication of big sparse matrices (stiffness and aerodynamic influence coefficient matrices). Mainly I have to multiply such ...
355 views

### Optimization on the manifold of stochastic matrices

So I have an optimization problem of the form $$\text{maximize}\hspace{3mm}f(A):{\bf R}^{K\times K}\rightarrow{\bf R}$$ $$\text{subject to}\hspace{19mm}A^T{\bf 1}=\bf{1}$$ $$\hspace{33mm}A\geq 0$$ ...
116 views

### Using entropy functions for increasing numerical stability

Regarding the numerical stabilization of two-dimensional advection equation, \dfrac{\partial f}{\partial t} + \Big(\dfrac{d\varepsilon_1(k)}{dk}\Big)\dfrac{\partial f}{\partial z} - \...
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### Conjugate residual/gradient convergence checking in practice

Let's say we want to solve $Ax=b$ ($A$ symmetric positive /semi/definite) with the conjugate residual/gradient method. $A$ comes from FEM where the mesh is being refined. The exact solution is $x_*$ ...
236 views

### Sound Waves Simulation in 3D Environment

I want to do a simulation of sound waves including wave propagation, absorption, and reflection in 3D space. I did some research and I found this question in stackoverflow but it talks about ...
234 views

### Negative viscosity stabilized by fourth order terms

I am trying to solve a "Navier-Stokes"-type problem where the viscosity is negative. Of course this renders the equation unstable and thus I add a fourth order term, so the entire equation becomes: ...
115 views

### What are the governing equations solved in coupled atmosphere-ocean models?

In (hydrostatic) atmospheric general circulation models, for example the so-calle Primitive Equations, consisting of the horizontal momentum equation, the hydrostatic balance, the continuity equation, ...
335 views

### Understanding the meaning of Computational Order of Convergence

I am a postgraduate student with interest in numerical methods for solving nonlinear systems of equations. I have read some papers that discussed about 'computational order of convergence' for some ...
1k views

### Using MINPACK for curve fitting: implementation?

I need to implement a non-linear fitting algorithm in Fortran and chose to use MINPACK's flavor of the Levenberg-Marquardt algorithm as a basis for the least-squares stuff. However, I seem to ...
79 views

### Order of convergence of Scrodinger eq. with CN scheme

I'm trying to solve numerically the 1-dim time dependent Schrodinger equation using the Crank Nicolson scheme and the Thomas algorithm to solve the tridiagonal matrix. The physical system consists of ...
556 views

### frozen coefficient vs. constant coefficient

This is a follow up to the question about the method of frozen coefficients. I think it deserves to be a separate question. The frozen coefficient problems are obtained by fixing the coefficients of ...
192 views