I am writing a code for steady state heat transfer on a rectangular domain. I am specifying temperature on the edges - nonzero Dirichlet boundary condition. The equations can be written in form of
$$KT=Q$$ $K$ is conductivity matrix, $T$ is unknown nodal temperature vector, and $Q$ is thermal load vector consisting of internal heat generation. For example, the system can look like
$$\begin {bmatrix} K_{11} & K_{12} & K_{13} & \dots & K_{1N}\\ K_{21} & K_{22} & K_{23} & \dots & K_{2N}\\ \vdots\\ K_{N1} & K_{N2} & K_{N3} & \dots & K_{NN} \end{bmatrix} \begin {bmatrix} 100\\ 200\\ \vdots\\ T_N \end{bmatrix} = \begin {bmatrix} Q_1\\ Q_2\\ \vdots\\ Q_N \end{bmatrix} $$
Non zero temperatures are applied on the edges of the rectangular domain (non-homogeneous Dirichlet boundary condition). How can I handle computationally non-zero Dirichlet boundary condition to solve for unknown temperature vector?