Let $\kappa$ be regular and $\lambda\geq\kappa$. For $f, g\in\kappa^\lambda$ say that $f\le^* g$ if the set $\{\gamma<\lambda:f(\gamma)>g(\gamma)\}$ has size less than $\kappa$. Set

$\mathfrak{b}_\kappa^\lambda:=\min\{|F|:F\subseteq \kappa^\lambda\text{ and }\neg\exists y\in \kappa^\lambda\forall x\in F(x\leq^* y)\}$,

$\mathfrak{d}_\kappa^\lambda:=\min\{|D|:D\subseteq \kappa^\lambda\text{ and }\forall x\in \kappa^\lambda\exists y\in D(x\leq^* y)\}$.

I'm studying the cardinals $\mathfrak{b}_\kappa^\lambda$ and $\mathfrak{d}_\kappa^\lambda$. My question what forcing should I use to use to increase $\mathfrak{b}_\kappa^\lambda$ and $\mathfrak{d}_\kappa^\lambda$?

For example: If $\lambda\geq\kappa$, $\mu>\lambda$ and $\mathrm{cf}(\mu)>\lambda$. What forcing can I use for $\mathfrak{d}_\kappa^\lambda\geq\mu$?