yuan-energy / small_tensor

A high performance small tensor library for inelastic finite element simulation

Small Tensor Library

This is a small tensor library which supports full Einstein notations.

The implementation is based on explicit SIMD intrinsics function for the bare-metal performance.

Small Tensor without heap memory in Runtime.

Simple usage example for 3 by 3 matrix:

tensor2<double,3,3> stress;

This is useful is either of the following cases:

• Avoid the malloc in the runtime.
• Since the data is kept in-place, you can save extra cache miss in the common case.

Why this library might be useful to you

To do fast tensor operations, one needs to write them in C/Fortran code style for performance. This means that one needs to use several "for loops" in order to do the products and sums component-wise.

Although computationally efficient, this type of programming style is error prone and makes codes lenghtier and hard to be debugged.

With small tensor library, we get the performance of a C code style combined with the code clarity and simplicity given by indicial tensor notation.

To perform tensor operations with small-tensor, one just needs to write in the .cpp the following "exactly replicate" code:

using namespace smalltensor ;
eindex<'i'> i; eindex<'j'> j; eindex<'k'> k; eindex<'l'> l;

A double contraction of a 4th-order tensor stiffness with a 2nd-order tensor strain can be written simply as:

stress(i,j)=stiffness(i,j,k,l)*strain(k,l);

API Examples

Declaration.

using namespace smalltensor ;
tensor1<double,10> vec;
tensor2<double,3,3> stress;
tensor3<double,2,3,3> cosserat; 
tensor4<double,3,3,3,3> stiffness;

Einstein Notations.

A(i,j) = B(i,k) * C(k,j) ;

All APIs for Einstein notations are available here

Performance