# All Questions

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### How to Run MPI-3.0 in shared memory mode like OpenMP

I am parallelizing code to numerically solve a 5 Dimensional population balance model. Currently I have a very good MPICH2 parallelized code in FORTRAN but as we increase parameter values the arrays ...
3k views

### Comparing Jacobi and Gauss-Seidel methods for nonlinear iterations

It is well known that for certain linear systems Jacobi and Gauss-Seidel iterative methods have the same convergence behavior, e.g. Stein-Rosenberg Theorem. I am wondering if similar results exist for ...
313 views

### Operator Splitting methods for DAEs

After doing some research, I've found that most of the literature on operator splitting methods (e.g. Strang Splitting, Fractional Step, etc.) are specifically designed for a standard problem type of ...
330 views

### For noisy or fine-structured data, are there better quadratures than the midpoint rule?

Only the first two sections of this long question are essential. The others are just for illustration. Background Advanced quadratures such as higher-degree composite Newton–Cotes, Gauß–Legendre, ...
453 views

### Fast Eigenvalue and SVD Solver for Structured Matrices

I am looking for a fast Eigenvalue and SVD solver for small dense structured matrices (Hankel and Toeplitz). I have searched for efficient implementations in libraries like MKL but I am not able to ...
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### Numerical integration using interval arithmetic, nowadays

Is there now a package for rigorous numerical integration that uses interval arithmetic and has access to a well-developed library of special functions? By "well-developed", I mean something that, at ...
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### Potential Reduction and Primal Path following methods

In both the potential reduction and primal path following interior point methods for linear programming, a barrier function is constructed which contains the terms $-\sum \log x_j$ where $x_j$ are the ...
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Given a fat matrix $B \in \mathbb{C}^{n \times m}$ (where $m > n$) with full row rank, I would like to find (numerically) a full-rank matrix $A$ that minimizes the Frobenius norm of the product $A ... 0answers 315 views ### Understanding Boundary Condition in FEM I am trying to understand Dirichlet and Neumann boundary conditions in FEM and I wanted to know if my inference is correct. To articulate my understanding, lets consider a simple case of TE and TM ... 0answers 122 views ### Do practice and theory differ substantially when implementing Neumann Boundary Conditions using a Mixed Method? I have implemented a pretty straightforward finite element solver for the following Poisson equation. For the purposes of this question we can assume the source term and the Dirichlet data both ... 0answers 117 views ### Good numerical method for solving the Kadomtsev Petviashvili equations. Is there an analytical solution? I need to solve the Kadomtsev Petviashvili (KP) equations $$\partial_x(\partial_t u+u \partial_x u+\epsilon^2\partial_{xxx}u)+\lambda\partial_{yy}u=0$$ where $$\lambda=\pm 1 \;.$$ My questions ... 0answers 216 views ### Will penalty-augmented stiffness matrix cause numerical issues in eigenvalue analysis? In the finite element method, we often construct the constraints of the system by adding penalty-function terms ( which often are many many magnitudes, up to$10^6\$ order bigger than the largest ...

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