# All Questions

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### Shape functions in Euler Bernoulli Beam Equation

Does anyone have a intuitive explanation of why Hermite polynomials have to be utilized as the shape functions in the FEM solution of the Euler Bernoulli Beam 4th order ODE? I have been learning FEM ...
8 views

### How to set initial guess to iterative solver in COMSOL?

How to set the initial guess for the iterative solver GMRES or FGMRES for linear problems (Helmholtz equation of RF module) in comsol?
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### Integrators for Nonlinear/Stiff PDE

It was suggested I ask this question in this section. Anyway: I have a particular nonlinear PDE of the form $$u_t(x,t)=iu_{xx}(x,t)+f(x,u(x,t)) \tag{1}$$ Where f is some nonlinear function. With ...
28 views

### WENO scheme on curvilinear coordinates

I've been developing a curvilinear FVM code. So far I've implemented the PPM scheme and am looking into adding WENO schemes. So far I've been discretizing the grid metrics using a second-order central....
31 views

### References to solve system of differential equations which describe the evolution of sandpile surface using the finite element method

I want to solve the following nonlinear system in 1D \begin{cases} \dot{R} + v \frac{\partial R }{\partial x} - \frac{\partial }{\partial x}\left( D \frac{\partial R }{\partial x} \right) -\Gamma =...
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### Efficient algorithm to determine the intersection volume of simple convex polyhedra

TLDR: Is there an efficient algorithm to compute the intersection of polyhedra with 8 or fewer vertices? I have two sets of FEM meshes for one geometry (one exhibiting a skin effect). I have to ...
29 views

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### Isosurface extraction when you know the derivatives

I have a complicated equation that defines a shape in 3D, and I would like to generate a surface mesh. The shape is defined by an isosurface, i.e. the function is positive inside the shape and ...
59 views

### Complex differentiation of linear solvers

I have a linear system $$Ax=b$$ which I'm solving approximately, and I need to take the frechet derivative of x with respect to z. Were I solving the problem exactly (either analytically or to machine ...
26 views

### turbulant flow modeling [on hold]

I have been trying to model the flow in a very thin channel using COMSOL Multyphysics. The laminar flow module does not converge no matter how I change the meshes, or use ramping loads and such. The k-...
27 views

### Duplicate Surface Meshes in different Gmsh files

My objective is to get a conformal surface mesh between two geometries meshed independently in different files. By example, I can start with a simple cube in one .geo file and mesh this geometry. ...
28 views

### How is the D value being updated at simple RRT algorithm?

I am studying the following lecture (image) regarding 5 iterations of the simple RRT algorithm. I am trying to understand how each value is being updated regarding each iteration. I have figured out ...
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### How to get started with numerically solving a Stochastic Navier Stokes equation

I originally posted the question on the math stackexchange, and was told I should try here. I’m researching Stochastic PDE, in particular the Navier Stokes Equation, and would like to estimate the ...