# All Questions

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### Matrix Calculation Different between Python and Matlab

I am transferring a finite element code from Matlab to Python. A problem occurs at the last step when I try to solve the displacement $U = F/K$. I have checked that the calculated $F$ and $K$ are same ...
69 views

### How to determine global stiffness matrix is constrained or not

Background In solid fem, we often solve $$\mathbf{Ku}=\mathbf{p}$$ where $\mathbf{K}$ is global stiffness matrix, $\mathbf{u}$ is displacement, $\mathbf{p}$ is global load vector. If displacement not ...
75 views

### How to use 8-cores CPU as a single-core more (8x) powerful CPU?

I use python for my algorithm which uses only one core and I need more processing speed. I have i7 6700K CPU with 8 cores. How to convert them to one core to have a total performance of 8 cores? ...
46 views

### 4th order tensor rotation - sources to refer

I am trying to model a linear elastic material in Abaqus using UMAT. For my application, I need to rotate the 6x6 compliance matrix for a given set of eigenvectors (or a rotation matrix). I came ...
29 views

### Discretization formula for a system of two differential equations. “Solution to one of these is the initial condition of the other”. In which sense?

Consider the following stochastic differential equation $$dy=\left(A-\left(A+B\right)y\right)dt+C\sqrt{y\left(1-y\right)}dW\tag{1}$$ where $A$, $B$ and $C$ are parameters ...
64 views

### How avoid square shape with Laplacian operator in reaction diffusion calculations?

I have used different variants of the Laplacian operator (div grad) using 4, 8, 12, 20 and 24 of the closest points. I get problems due to the chosen coordinate system and the discretization of the ...
31 views

### Convergence of Truncated Newton for non-convex Hessian

I was wondering if anyone could enlighten me about the convergence properties of the truncated newton method in case of a non-positive definite hessian $\nabla^2 f = H$. From the Book 'Numerical ...
34 views

### traction boundary conditions in elasticity

I have a question about implementing traction boundary conditions in 2D and 3D linear elasticity. Consider the picture above. I want to apply traction boundary conditions on the boundary in red. My ...
43 views

### python plot exhibiting delta function behaviour but it was not supposed to do it

I'm currently trying to plot the photoionization cross-section in a semiconductor. The photoionization process is an optical transition of an electron in the ground state to higher subbands in a ...
63 views

### How is the final result calculated in RK-Dopri(4,5)?

I have found a toy implementation of RK-Dopri(4,5), written in Python. I am concerned however, about line 118: y = y + h * (b1*K1+b3*K3+b4*K4+b5*K5+b6*K6) Has the ...
90 views

### Optimization of expensive model with many parameters

I have a physical model which takes $\sim50$ parameters and gives $\sim2000$ outputs taking tens of minutes to run. I need to optimize these parameters to give outputs as close as possible to data. ...
31 views

### Why is Time evolving block decimation so efficient?

I have a short question about Time evolving block decimation (TEBD). During a lecture I was told that this method is very efficient in evolving 1D quantum spin systems with only nearest neighbor ...
70 views

### Pros of Fourier-Galerkin spectral methods

What are the pros of Fourier-Galerkin spectral methods while solving PDEs? Here's the one that came in my mind first: Easy implementation: using this method, differentiation operator computation is ...
69 views

### Numerical linear algebra paper - Confusion about $LDL^T$ factorization for preconditioning

I came across this paper by Simoncini and Popolizio that deals with acceleration techniques in the context of rational Chebychev approximation for the exponential. The problem is to solve efficiently ...
130 views

### Flux sign and face normal confusion in finite volume method

I implemented a solver for the 2D steady-state heat equation (without heat generation and homogeneous material) $\nabla. (k\nabla T) = 0$, using finite volume method, however, I am having some ...
59 views

### Reading VTK file into C++ for analysis

I apologize in advance if this post is at all ignorant or elementary, I am a pure mathematician who is newly getting into the world of scientific computing. For my research, my advisor would like me ...
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### How to calculate error in successive over relaxation for PDE?

I am trying to solve the Poisson equation numerically using the FDM method in C++. But I have a little confusion with the iterative process. I understand that the number of iterations should go until ...
55 views

### coarsening coefficient matrixes (A2h, A4h…) for geometric multigrid method in 2-D/3-D

I am learning about multigrid methods from the textbook section 6.3 Multigrid Methods, which shows a geometric multigrid algorithm for 1-D examples in detail, including how to build restriction/...
90 views

### Calculating the Strange Attractor of the Duffing Oscillator in C++

I am simultaneously trying to learn computational physics methods, chaos, and C++. I think this is the right site for the question, and I apologise if not. I started working through Thijssen's ...
158 views

### Numerical solution of high-dimensional integral involving positive-part function

Consider a potentially high-dimensional (say, $N$ up to 20) integral of the form $$\int_0^\infty \rho_1(x_1)\rho_2(x_2) \cdots \rho_N(x_N) \bigg(x_1+x_2+\cdots+x_N -K\bigg)^+ \, dx_1 \cdots dx_N.$$ ...
169 views

### Different questions about “Inverse Physics problems”

I am in a context of forecasts in astrophysics. Don't be too rude if questions seem to you stupid or naive but rather indulgent, I am just looking for better undertsand all these numerical methods of ...
43 views

### How match memory to CPU with NUMA?

I have a multiple CPU system weakly connected and memory access is slow when one CPU accesses the others memory. The CPUs uses NUMA. How can I make TensorFlow adjust to this or does it per default?
53 views

### Which are the right configurations in the Markov chain of a Hamiltonian Monte Carlo algorithm?

I have a question about the Markov Chain Hamiltonian Monte Carlo (MCHMC). Hamiltonian Monte Carlo is known as Hybrid Monte Carlo too. I'll describe the steps of the algorithm. We have at the ...
28 views

### How to generate a symmetric matrix that will produce a pos-def matrix after application of a pos-def kernel function?

Note in advance that I'm not trying to sample symmetric, positive-definite matrices - that, at least, I know how to do. What I'd like to sample, is symmetric matrices (ideally with diagonal 0, ...
36 views

### Running VTK simulation on Visit

I apologize if any of these questions are elementary, I have just begun research involving scientific computing and am still getting ahold of the basics. My research advisor has given me a few ...
46 views

### Choosing good modelling method for solving Boltzmann equation

I'm writing a solver for Boltzmann Equations (BE) including a force term in rarefied plasma, for my PhD. The aim is to see if an instability occurs inside an electric streamer (theoretically it should,...
69 views

### RK4-method starts oscillating above certain input parameters

I am trying to solve an equation of the following type $$\partial_zE(z)=-c_0J$$ with $$J=c_1\beta E^3(z)$$ using the boost::odeint-framework and a fixed time stepper, with $c_0$, $c_1$ and $\beta$ ...
61 views

### Uniaxial stretching solution not uniform in FEM code

I am trapped here for a long time. I wrote a toy Matlab FEM code. I want to run the follow simulation. Mesh Suppose we have a cube, and we divide it into subcube along $x,y,z$ axis, then each subcube ...
58 views

### Can we apply time-parallel methods in case of peridynamics?

Can we solve peridynamics in parallel for time-dimension using methods like MGRIT? This method can be applied for time dependent PDEs, however, since peridynamics is a non-local approach, can this ...
11 views

### Using spline or piece wise function as input (intermediate) in Gekko

Simple paraphrase of my question is what is the best way to use a table or curve as an input for an optimization problem in Gekko (and/or AP Monitor)? For example, I have simplified atmospheric ...
20 views

### Hawkes Process : recursive formula for : $R'_{m,n} (k) = \sum_{ \{i : t_i^n < t_k^m \} } (t_k^m - t_i^n) \exp ( - \beta_{m,n} ( t_k^m - t_i^n ) )$

Following the advice of a fellow mathematician, I am asking my question here from (https://mathoverflow.net/questions/365554/hawkes-process-recursive-formula-for-r-m-n-k-sum-i-t-in-t) I need to use a ...
60 views

https://www.jstor.org/stable/pdf/2157482.pdf, here I have a problem in last equation of (2.6) in section (2.1). When they are considering error equation on the interface $\Gamma$ they get $e_v^{(n)} = ... 1answer 82 views ### Which scheme for inhomogeneous convection-diffusion equation with highly variable coefficients? I have a 1D convection-diffusion equation$\sigma_t = a(x,t) \sigma_{xx}+b(x,t)\sigma_x+f(x,t)$defined on the unit interval, with nonzero Neumann boundary conditions at both ends. It should be noted ... 0answers 18 views ### Benchmark instances for directed 3-Cycle cover The directed 3-Cycle cover asks for a vertex-covering set of oriented cycles with at least three vertices per cycle such that every vertex is covered by exactly one cycle. I have scrutinzed the ... 2answers 114 views ### How to begin writing scientific codes in C++ in Trilinos or PETSC style? My background: I have taken some courses on numerical analysis during my PhD and read a few books on the topic as well. I mostly work on low Reynolds number fluid mechanics and use boundary element ... 1answer 1k views ### How to document math formulations in scientific computing codes? I am writing the code relate to math. There is some complicated math formulation in the project. Directly writing the calculation code leads to hard understanding; thus I want to comment on the ... 1answer 28 views ### Getting streamline for a lid driven cavity flow in openFoam/ParaView I have installed openFoam on Debian GNU/Linux and learning from official user guide. I have a problem with generating streamlines. I am trying to generate streamlines as explained in the post ... 0answers 66 views ### Computation of a functional for large values Consider the following function : $$f(x) = \sin^2(\frac{π\Gamma(x)}{2x})$$ Now consider the following functional : $$I(x)=\int_0^\infty \frac{f(x + iy) − f(x − iy)}{e^{2πy}-1} dy$$ I need values for ... 0answers 41 views ### Adaptive quadrature methods for Fourier Optics In Fourier Optics one often needs to compute approximations to bivariate integrals like $$\int_{-\frac{l}{2}}^{\frac{l}{2}}\int_{-\frac{l}{2}}^{\frac{l}{2}} {\rm e}^{i\phi(\xi,\eta)}\mathrm{exp}\left[... 1answer 87 views ### Calculate stable time step DG method for advection-diffusion For stable time steps for the RKDG method for transport equations we require that$$ \Delta t \le \frac{\Delta x CFL}{(2k + 1)|\lambda|},$$where$\lambda$is the eigenvalue of our conservation law ... 1answer 90 views ### Solving large sparse system I am working on a problem with very large sparse matrices. I'd like to compute$A^{-1} B$, that is a crucial part of converting DAE to ODE (and there is no workaround). Here size of$A$is 2E+5 x 2E+5 ... 1answer 119 views ### How GMRES method finds smallest singular value and the corresponding singular vectors of a matrix? https://stackoverflow.com Krylov solvers for iterative computation of the smallest singular value and the corrensponding singular vectors of a matrix Edit: This is a follow-up question to How to ... 0answers 11 views ### Sufficient conditions to ensure divergence of a sequence in Maxima I am using Maxima to check whether a given sequence is diverging to$+\infty$. I know that this problem is undecidable and we note that Maxima is throwing an error: ... 1answer 80 views ### Efficient projection of a vector onto matrix kernel Given an$m \times n$matrix$A$and a vector$x\in\mathbb R^n$, with$m<n$, what's an efficient way of computing the projection of$x$onto the kernel of$A\$?

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