# Questions tagged [sparse-matrix]

Questions related to storage, assembly, operations, and other aspects of dealing with sparse matrices, for which only non-zero elements are stored. Questions that do not with sparse matrices directly, but other means of using sparsity should be tagged with [sparse-operator].

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### Problems on the algebraic theory of sparse matrices

I have finished testing basic large densely parallel matrix multiplication on 4 gpu's ,and have done work on TSLU and TSQR on cpu's based on mpi. I am going to continue working on the theory of ...
131 views

### Fast Fourier Transform on Meshes

I have a (closed, manifold, oriented) triangular mesh for which I build a matrix $L\in\mathbb{R}^{n\times n}$ discretising the negated Laplace-Beltrami operator. The matrix $L$ is symmetric positive ...
129 views

### Right blocked linear equation solver on Dense Algebra and Sparse Algebra

I have implemented 1D mesh parallel QR decomposition and LU decomposition,I would like to ask if a linear equation Ax=b,b is a large matrix and I need to shard b or Shard A,b at the same time. Is ...
299 views

### How to efficient solve $e^{-tA} x =b$, where A is a very sparse matrix

I am going to solve an equation containing an exponential matrix $e^{tA} x =b$, which can be obtained naturally through $x=e^{-tA} b$. A is a 1million $\times$ 1 million matrix with stores 7.15 ...
1 vote
125 views

### Solving 2D Poisson equation with mixed boundary conditions in Python

I am trying to numerically solve the Poisson's equation $$u_{xx} + u_{yy} = - \cos(x) \quad \text{if} - \pi/2 \leq x \leq \pi/2 \quad \text{0 otherwise}$$ The domain is the rectangle with vertices ...
1 vote
122 views

### Are there good block sparse matrix solver libraries?

There are some great libraries with linear solvers for sparse matrices - SuiteSparse is the obvious one. The methods work on sparse matrices with scalar entries. However, often in optimization ...
146 views

### Solving Poisson's equation without a Dirichlet boundary condition

Some context of what I am trying to do: I am trying to implement a function that uses the heat method to calculate geodesic distances in a tetrahedral mesh, and I want to calculate the distances for ...
38 views

### Diagonalization of large sparse matrix, computational programme recommendation and methods

According to this link, All eigenpairs of large sparse symmetric matrix. The guy @Baranas seems to have given a very confident answer about solving the whole Eigen spectrum. May I know if anyone has ...
101 views

### What is the difference between approximations of mixed derivative and how to implement it

currently I am solving 2D nonlinear second order differential equation containing mixed derivative. I started searching how to descretisize it and found two formulas for 4th order approximation. First ...
202 views

### Accelerating the computation of scipy.sparse.linalg.expm_multiply

I have a tridiagonal antiHermitian matrix ($-i*Hami*t$) with nonzero elements only along the upper diagonal and lower diagonal, and the goal is to know the action of exponential of such matrix on a ...
148 views

### How to efficiently fill in, in parallel, a PETSc matrix from a COO sparse matrix?

Considering the following COO sparse matrix format, with repeated indices: ...
1 vote
144 views

### Crank Nicolson Method with closed boundary conditions

I want to simulate 1D diffusion with a constant diffusion coefficient using the Crank-Nicolson method. $$\frac{\partial u (x,t)}{\partial t} = D \frac{\partial^2 u(x,t)}{\partial x^2}.$$ I take an ...
391 views

1 vote
157 views

### What is the difference between Adittive Schwarz as a preprocessor and a solver?

As we all know, the Additive Schwarz approach can be used as either solver or preconditioner, however, my question is, what is the difference between the two? In other words, how to use AS as solver, ...